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

The answer to (\partial)/(\partial x)((x^3-y^2)^2) is 6x^2(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 x)((x^3-y^2)^2)

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

6 x^{2} (x^{3} - y^{2})

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 6 x^{2} (x^{3} - y^{2})

\frac{\partial}{\partial x} ((x + y)^{5})

y = 1 - x^{2}, y = x - 1

\int 3 sin (d) x d x

\int_{- 1}^{3} (- x)^{3} d x

g (x) = x^{2} (1 - 6 x)

What is (\partial)/(\partial x)((x^3-y^2)^2) ?
The answer to (\partial)/(\partial x)((x^3-y^2)^2) is 6x^2(x^3-y^2)