What is the d/(dy)(2xe^{xy}+x^2ye^{xy}) ?

The d/(dy)(2xe^{xy}+x^2ye^{xy}) is 3e^{xy}x^2+e^{xy}x^3y

What is the first d/(dy)(2xe^{xy}+x^2ye^{xy}) ?

The first d/(dy)(2xe^{xy}+x^2ye^{xy}) is 3e^{xy}x^2+e^{xy}x^3y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

3 e^{x y} x^{2} + e^{x y} x^{3} y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

2 x^{2} e^{x y} + x^{2} (e^{x y} + x e^{x y} y) : 3 e^{x y} x^{2} + e^{x y} x^{3} y

= 3 e^{x y} x^{2} + e^{x y} x^{3} y

What is the d/(dy)(2xe^{xy}+x^2ye^{xy}) ?
The d/(dy)(2xe^{xy}+x^2ye^{xy}) is 3e^{xy}x^2+e^{xy}x^3y
What is the first d/(dy)(2xe^{xy}+x^2ye^{xy}) ?
The first d/(dy)(2xe^{xy}+x^2ye^{xy}) is 3e^{xy}x^2+e^{xy}x^3y