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Solve the given problems by finding the appropriate derivative.In an electronic device, the maximum current density $i_{m}$ as a function of the temperature $T$ is given by $i_{m}=A T^{2} e^{k / T},$ where $A$ and $k$ are constants. Find the expression for a small change in $i_{m}$ for a small change in $T$.

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 8

Applications

Derivatives

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We need to find the expression for the charge, uh, And has given to us to the 80 square times E. To the k O T for charge for small charges and see, so we have to find the first derivative of the maximum current density. So the Eye over DT, both equal to a tom's t square times eating Katie cable, T times, Katie times negative K over T squared plus into the k t K over tea times two. That gives me a get the out. You have the K. We get 5:00 a constant. So that gives us negative K times. Even the king of the team close to see times E to the K over two.

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