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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

\int \frac{x}{2 x ^{2} + 3} d x

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

\int \frac{x ^{2} + 3 x + 7}{x} d x

d er i v a t i v e y = 5 x^{2} e^{2 x}

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

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