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Step-by-step Solution

Derive the function e^(xy*ln(x)) with respect to x

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Answer

$x\frac{1}{x}$

Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(e^{xy\cdot \ln\left(x\right)}\right)$
1

Applying the derivative of the exponential function

$1e^{xy\ln\left(x\right)}\cdot\frac{d}{dx}\left(xy\ln\left(x\right)\right)$
2

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$ye^{xy\ln\left(x\right)}\cdot\frac{d}{dx}\left(x\ln\left(x\right)\right)$

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Answer

$x\frac{1}{x}$
$\frac{d}{dx}\left(e^{xy\cdot \ln\left(x\right)}\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.47 seconds

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