What is (\partial)/(\partial y)(e^x+ye^{xy}) ?

The answer to (\partial)/(\partial y)(e^x+ye^{xy}) is e^{xy}+e^{xy}xy

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(e^x+ye^{xy})

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

e^{x y} + e^{x y} x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (e^{x}) = 0

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

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

Simplify

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

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

\frac{d y}{- y ln ( \frac{y}{k} )} = c d x

\frac{d y}{d x} + 3 y = 30

y^{^{''}} + 9 y = - 6 tan (3 x)

\frac{d}{d x} ((2) (e^{3 x}))

What is (\partial)/(\partial y)(e^x+ye^{xy}) ?
The answer to (\partial)/(\partial y)(e^x+ye^{xy}) is e^{xy}+e^{xy}xy