What is (\partial)/(\partial y)(x^4y^3+8x^2y) ?

The answer to (\partial)/(\partial y)(x^4y^3+8x^2y) is 3x^4y^2+8x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial y)(x^4y^3+8x^2y)

\frac{\partial}{\partial y} (x^{4} y^{3} + 8 x^{2} y)

3 x^{4} y^{2} + 8 x^{2}

Solution steps

\frac{\partial}{\partial y} (x^{4} y^{3} + 8 x^{2} y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{4} y^{3}) + \frac{\partial}{\partial y} (8 x^{2} y)

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

\frac{\partial}{\partial y} (8 x^{2} y) = 8 x^{2}

= 3 x^{4} y^{2} + 8 x^{2}

What is (\partial)/(\partial y)(x^4y^3+8x^2y) ?
The answer to (\partial)/(\partial y)(x^4y^3+8x^2y) is 3x^4y^2+8x^2