What is (\partial)/(\partial x)((x^3-y^2)^{(-1)}) ?

The answer to (\partial)/(\partial x)((x^3-y^2)^{(-1)}) is -(3x^2)/((x^3-y^2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)((x^3-y^2)^{(-1)})

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( x ^{3} - y ^{2} ) ^{2}} \cdot 3 x^{2} : - \frac{3 x ^{2}}{( x ^{3} - y ^{2} ) ^{2}}

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

\frac{d}{d x} (4 x^{2} + 3 x + 2)

d er i v a t i v e y = e^{e}

\int x^{2} (1 - x) d x

\int \frac{sin ( x )}{x} d x

\int_{0}^{1} \frac{1}{( 2 x - 3 ) ^{2}} d x

What is (\partial)/(\partial x)((x^3-y^2)^{(-1)}) ?
The answer to (\partial)/(\partial x)((x^3-y^2)^{(-1)}) is -(3x^2)/((x^3-y^2)^2)