## Related questions with answers

Question

Find df/dx if

$f(x)=\int_{1}^{e^{x}} \frac{2 \ln t}{t} d t.$

Solution

VerifiedAnswered 8 months ago

Answered 8 months ago

Step 1

1 of 2First, we can find $\dfrac{df} {dx}$ as follows:

$\begin{align*} \frac{df}{dx} &= \frac{d}{dx} \qty(\int_{1}^{e^x} \frac{2\ln t}{t} \ dt) \\ \\ &= \frac{2\ln e^x}{e^x} \frac{d}{dx} \qty(e^x) = \frac{2x \ln e}{e^x} e^x \\ \\ \therefore \ \ \ \frac{df}{dx} &= 2x \ \ \ \ \ \ \ \ (1) \end{align*}$

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