What is (\partial)/(\partial x)(e^{x*ln(y)}) ?

The answer to (\partial)/(\partial x)(e^{x*ln(y)}) is y^xln(y)

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(\partial)/(\partial x)(e^{x*ln(y)})

\frac{\partial}{\partial x} (e^{x \cdot l n (y)})

y^{x} ln (y)

Solution steps

\frac{\partial}{\partial x} (e^{x l n (y)})

Simplify

e^{x l n (y)} : y^{x}

= \frac{\partial}{\partial x} (y^{x})

Treat

y

as a constant

Apply the derivative exponent rule:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= y^{x} ln (y)

What is (\partial)/(\partial x)(e^{x*ln(y)}) ?
The answer to (\partial)/(\partial x)(e^{x*ln(y)}) is y^xln(y)