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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- yz x^{- z - 1}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

= - yz x^{- z - 1}

x \to 1.001 lim (x^{2} - 2 x - 1)

\int_{2}^{4} x^{3} d x

\int e^{x} 5 - e^{x} d x

\frac{x ^{2} - 3 x - 4}{x - 2}

\int 2 cos^{2} (x) sin (x) d x

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