What is (\partial)/(\partial z)(xe^{y-z^2}) ?

The answer to (\partial)/(\partial z)(xe^{y-z^2}) is -2e^{y-z^2}xz

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial z)(xe^{y-z^2})

\frac{\partial}{\partial z} (x e^{y - z^{2}})

- 2 e^{y - z^{2}} x z

Solution steps

\frac{\partial}{\partial z} (x e^{y - z^{2}})

Treat

x, y

as constants

Take the constant out:

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

= x \frac{\partial}{\partial z} (e^{y - z^{2}})

Apply the chain rule:

e^{y - z^{2}} \frac{\partial}{\partial z} (y - z^{2})

= e^{y - z^{2}} \frac{\partial}{\partial z} (y - z^{2})

\frac{\partial}{\partial z} (y - z^{2}) = - 2 z

= x e^{y - z^{2}} (- 2 z)

Simplify

= - 2 e^{y - z^{2}} x z

\frac{d}{d x} (5 x + x^{2})

x \to 5 + lim (5 x - 5)

\frac{\partial}{\partial t} (t^{2} e^{- x})

\frac{1}{s ^{2} + s + 1} \cdot \frac{1}{s}

\frac{d}{d x} (1 - 5 x)

What is (\partial)/(\partial z)(xe^{y-z^2}) ?
The answer to (\partial)/(\partial z)(xe^{y-z^2}) is -2e^{y-z^2}xz