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

The answer to (\partial)/(\partial x)(e^{sqrt(x)}ln(y)) is (e^{sqrt(x)}ln(y))/(2sqrt(x))

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

\frac{\partial}{\partial x} (e^{x} ln (y))

\frac{e ^{x} ln ( y )}{2 x}

Solution steps

\frac{\partial}{\partial x} (e^{x} ln (y))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

e^{x} \frac{\partial}{\partial x} (x)

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

\frac{\partial}{\partial x} (x) = \frac{1}{2 x}

= ln (y) e^{x} \frac{1}{2 x}

Simplify

ln (y) e^{x} \frac{1}{2 x} : \frac{e ^{x} ln ( y )}{2 x}

= \frac{e ^{x} ln ( y )}{2 x}

What is (\partial)/(\partial x)(e^{sqrt(x)}ln(y)) ?
The answer to (\partial)/(\partial x)(e^{sqrt(x)}ln(y)) is (e^{sqrt(x)}ln(y))/(2sqrt(x))