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

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

Popular >

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{1}^{2} \frac{9 ln ( x )}{x ^{2}} d x

f (x) = x^{2} - \frac{1}{x}, at x = 2

\frac{d}{d y} (e^{\frac{y}{x}})

y^{^{'}} = \frac{( e ^{x} )}{y}

\int (e^{3 x} - 1)^{3} d x

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