Equations Involving Derivatives - AP Calculus BC

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Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

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Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

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Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Question

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

Tap to reveal answer

Answer

To find the heat flux, we must find the change in temperature with respect to x:

$$\frac{\mathrm{d}$ T}{\mathrm{d} x}= $\frac{x}{6}$+3$

The derivative was found using the following rule:

$\frac{\mathrm{d}$ }{\mathrm{d} x} $x^n$$=nx^{n-1}$

Plugging this into Fourier's law, we get

$q=-k($\frac{x}{6}$+3)$

← Didn't Know|Knew It →

Knew It

Equations Involving Derivatives - AP Calculus BC

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by The heat flux is given by Fourier's law, , where k is a constant. Find the heat flux for the given profile.

To find the heat flux, we must find the change in temperature with respect to x: The derivative was found using the following rule: Plugging this into Fourier's law, we get

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.

The temperature profile of a system is given by

The heat flux is given by Fourier's law, $q=-k$\frac{\mathrm{d}$ T}{\mathrm{d} x}$ , where k is a constant.

Find the heat flux for the given profile.