If f(x) = x^2e^1/x, what is f'(1)?

Chain Rule, Log Differentiation & Rate of Change · Question 73 of 130

Question 73

MediumOriginal question

If $f(x) = x^{2}e^{1/x}$ , what is $f'\left(1\right)$ ?

- 2 e

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e

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2 e

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3 e

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$f'(x) = 2xe^{1/x} + x^{2}e^{1/x} \cdot \left(-\frac{1}{x^{2}}\right) = e^{1/x}(2x - 1)$ .
At 1: $e(2 - 1) = e$ .

Worth noting

$3e$ takes the derivative of $\frac{1}{x}$ as $+\frac{1}{x^{2}}$ ; it is $-\frac{1}{x^{2}}$ .

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.