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

The d/(d{y)}({x}^{({z})/({y)}}) is -(e^{\frac{ln({x}){z})/({y)}}ln({x}){z}}{{y}^2}

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

The first d/(d{y)}({x}^{({z})/({y)}}) is -(e^{\frac{ln({x}){z})/({y)}}ln({x}){z}}{{y}^2}

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{z}{y}})

- \frac{e ^{\frac{l n ( x ) z}{y}} ln ( x ) z}{y ^{2}}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d y} (\frac{z}{y} ln (x)) = - \frac{ln ( x ) z}{y ^{2}}

= e^{\frac{z}{y} l n (x)} (- \frac{ln ( x ) z}{y ^{2}})

Simplify

e^{\frac{z}{y} l n (x)} (- \frac{ln ( x ) z}{y ^{2}}) : - \frac{e ^{\frac{l n ( x ) z}{y}} ln ( x ) z}{y ^{2}}

= - \frac{e ^{\frac{l n ( x ) z}{y}} ln ( x ) z}{y ^{2}}

\frac{d}{d x} (65536 cos (2 x))

\int (16 x + 4) 8 x^{2} + 4 x d x

(3 x^{2} + 5) e^{4 x}

\int e^{c o s (9 t)} sin (9 t) d t

\int 6 + x^{2} d x

What is the d/(d{y)}({x}^{({z})/({y)}}) ?
The d/(d{y)}({x}^{({z})/({y)}}) is -(e^{\frac{ln({x}){z})/({y)}}ln({x}){z}}{{y}^2}
What is the first d/(d{y)}({x}^{({z})/({y)}}) ?
The first d/(d{y)}({x}^{({z})/({y)}}) is -(e^{\frac{ln({x}){z})/({y)}}ln({x}){z}}{{y}^2}