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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

2 x + 4 y^{3}

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = 2 x + y^{3}

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

\frac{\partial}{\partial y} (y) = 1

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

= 1 \cdot (2 x + y^{3}) + 3 y^{2} y

Simplify

1 \cdot (2 x + y^{3}) + 3 y^{2} y : 2 x + 4 y^{3}

= 2 x + 4 y^{3}

\int 5 - 4 x^{2} d x

\int x + sin (x) d x

\int \frac{x ^{3} + 33}{x ^{2} + 7 x + 12} d x

\int \frac{x + 1}{x ^{2} + 2 x + 7} d x

f (x) = 8 x^{5} - 8

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