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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{y}{x ^{3} + y ^{2}}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

\frac{1}{2 x ^{3} + y ^{2}} \frac{\partial}{\partial y} (x^{3} + y^{2})

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

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

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

Simplify

\frac{1}{2 x ^{3} + y ^{2}} \cdot 2 y : \frac{y}{x ^{3} + y ^{2}}

= \frac{y}{x ^{3} + y ^{2}}

x \to 5 - lim (\frac{1}{x - 5})

\frac{d}{d x} (m x)

\frac{\partial}{\partial x} (sin (x + 4 y))

\int sec^{2} (d) x d x

\int \frac{x + 3}{x ^{2} + 4} d x

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