What is (\partial)/(\partial x)(e^{xy^2}+4zy^3) ?

The answer to (\partial)/(\partial x)(e^{xy^2}+4zy^3) is e^{xy^2}y^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(e^{xy^2}+4zy^3)

\frac{\partial}{\partial x} (e^{x y^{2}} + 4 z y^{3})

e^{x y^{2}} y^{2}

Solution steps

\frac{\partial}{\partial x} (e^{x y^{2}} + 4 z y^{3})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (e^{x y^{2}}) + \frac{\partial}{\partial x} (4 z y^{3})

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

\frac{\partial}{\partial x} (4 z y^{3}) = 0

= e^{x y^{2}} y^{2} + 0

Simplify

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

What is (\partial)/(\partial x)(e^{xy^2}+4zy^3) ?
The answer to (\partial)/(\partial x)(e^{xy^2}+4zy^3) is e^{xy^2}y^2