What is the d/(d{y)}({x}^{({y})/({z)}}) ?

The d/(d{y)}({x}^{({y})/({z)}}) is (e^{\frac{ln({x}){y})/({z)}}ln({x})}{{z}}

What is the first d/(d{y)}({x}^{({y})/({z)}}) ?

The first d/(d{y)}({x}^{({y})/({z)}}) is (e^{\frac{ln({x}){y})/({z)}}ln({x})}{{z}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{e ^{\frac{l n ( x ) y}{z}} ln ( x )}{z}

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{\frac{y}{z}} = e^{\frac{y}{z} l n (x)}

= \frac{d}{d y} (e^{\frac{y}{z} l n (x)})

Apply the chain rule:

e^{\frac{y}{z} l n (x)} \frac{d}{d y} (\frac{y}{z} ln (x))

= e^{\frac{y}{z} l n (x)} \frac{d}{d y} (\frac{y}{z} ln (x))

\frac{d}{d y} (\frac{y}{z} ln (x)) = \frac{ln ( x )}{z}

= e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z}

Simplify

e^{\frac{y}{z} l n (x)} \frac{ln ( x )}{z} : \frac{e ^{\frac{l n ( x ) y}{z}} ln ( x )}{z}

= \frac{e ^{\frac{l n ( x ) y}{z}} ln ( x )}{z}

- sin (x^{2})

\int_{2}^{8} \frac{1}{2 x + 1} d x

\int_{0}^{1} 4 t d t

\int 3 x^{2} tan (y) - \frac{2 y ^{3}}{x ^{3}} d x

\int \frac{1}{( 2 x - 3 ) ^{2} + 1} d x

What is the d/(d{y)}({x}^{({y})/({z)}}) ?
The d/(d{y)}({x}^{({y})/({z)}}) is (e^{\frac{ln({x}){y})/({z)}}ln({x})}{{z}}
What is the first d/(d{y)}({x}^{({y})/({z)}}) ?
The first d/(d{y)}({x}^{({y})/({z)}}) is (e^{\frac{ln({x}){y})/({z)}}ln({x})}{{z}}