What is (\partial)/(\partial y)(e^{xy}+x^2z) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(e^{xy}+x^2z)

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

e^{x y} x

Solution steps

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

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (x^{2} z) = 0

= e^{x y} x + 0

Simplify

= e^{x y} x

\frac{x ^{4}}{1 - x ^{3}}

x^{2}, (- 2, 1)

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

\frac{d}{d x} ((4 x^{3} + 1)^{2})

\int sin^{2} (X) d X

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