What is (\partial)/(\partial z)(e^{xy}ln(z)) ?

The answer to (\partial)/(\partial z)(e^{xy}ln(z)) is (e^{xy})/z

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(\partial)/(\partial z)(e^{xy}ln(z))

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

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

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the common derivative:

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

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

Simplify

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

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

f (x) = 2 x^{3} + 5 x^{2}, at x = - 2

\frac{d}{d x} (\frac{a x + 1 + x}{x ^{2} - 1})

\frac{\partial}{\partial x} (2 x^{2} y e^{x} + 2)

x \frac{d y}{d x} + (2 x + 1) y = e^{- 2 x}

\int \frac{1}{5 x ^{2} + 20 x - 10} d x

What is (\partial)/(\partial z)(e^{xy}ln(z)) ?
The answer to (\partial)/(\partial z)(e^{xy}ln(z)) is (e^{xy})/z