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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(x^{y/(y+z)})

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Power Rule:

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

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

Simplify

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

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

f^{^{''}} (x) = x^{- 3} + π x^{2} - 2

f (x) = 2 x^{2} - 3 x, at x = 4

\frac{d}{d x} (\frac{4 x}{2 - x ^{2}})

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

\frac{\partial}{\partial x} (2 x^{2} + y^{2} - 9 y)

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