What is (\partial)/(\partial x)(e^{(xy)/(z^2)}) ?

The answer to (\partial)/(\partial x)(e^{(xy)/(z^2)}) is (e^{\frac{xy)/(z^2)}y}{z^2}

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(\partial)/(\partial x)(e^{(xy)/(z^2)})

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

\frac{e ^{\frac{x y}{z ^{2}}} y}{z ^{2}}

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (\frac{x y}{z ^{2}}) = \frac{y}{z ^{2}}

= e^{\frac{x y}{z ^{2}}} \frac{y}{z ^{2}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{e ^{\frac{x y}{z ^{2}}} y}{z ^{2}}

y^{^{''}} = \frac{2 k}{1 - k}

\frac{d}{d x} (x^{2} ln ∣ x ∣)

f (x) = \frac{x ^{2} + 2 x}{( x + 1 ) ^{2}}

\frac{\partial}{\partial x} (4 e^{yz} cos (x yz))

x \to 7 lim (\frac{- 2}{7 - x})

What is (\partial)/(\partial x)(e^{(xy)/(z^2)}) ?
The answer to (\partial)/(\partial x)(e^{(xy)/(z^2)}) is (e^{\frac{xy)/(z^2)}y}{z^2}