What is (\partial)/(\partial y)(e^xln(y)) ?

The answer to (\partial)/(\partial y)(e^xln(y)) is (e^x)/y

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(\partial)/(\partial y)(e^xln(y))

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

\frac{e ^{x}}{y}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the common derivative:

\frac{\partial}{\partial y} (ln (y)) = \frac{1}{y}

= e^{x} \frac{1}{y}

Simplify

e^{x} \frac{1}{y} : \frac{e ^{x}}{y}

= \frac{e ^{x}}{y}

\frac{d}{d y} (y sin (x y))

x^{2} + 4, - x^{2} - 1, [0, 1]

\frac{d y}{d x} = \frac{2 x y + 2 x}{x ^{2} + 1}

\int_{1}^{\infty} \frac{1}{x ^{8}} d x

\frac{\partial}{\partial x} (4 x y - 3 x^{2})

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