What is (\partial)/(\partial x)((xy)^z) ?

The answer to (\partial)/(\partial x)((xy)^z) is zy^zx^{z-1}

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(\partial)/(\partial x)((xy)^z)

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

z y^{z} x^{z - 1}

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

z (x y)^{z - 1} \frac{\partial}{\partial x} (x y)

= z (x y)^{z - 1} \frac{\partial}{\partial x} (x y)

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

= z (x y)^{z - 1} y

Simplify

z (x y)^{z - 1} y : z y^{z} x^{z - 1}

= z y^{z} x^{z - 1}

\int \frac{x ^{3} - x ^{2} - 4 x + 4}{x ^{3} - x ^{2} - 6 x} d x

\frac{\partial}{\partial x} (e^{2 y} cos (3 x))

3

y^{^{''}} - 5 y^{^{'}} + 6 y = x \cdot e^{(- 4 \cdot x)}

\frac{d}{d x} (\frac{5}{( 2 x ) ^{3}})

What is (\partial)/(\partial x)((xy)^z) ?
The answer to (\partial)/(\partial x)((xy)^z) is zy^zx^{z-1}