What is the derivative of (x^2/(y^2)) ?

The derivative of (x^2/(y^2)) is (2x(-x\frac{dy)/(dx)+y)}{y^3}

What is the first derivative of (x^2/(y^2)) ?

The first derivative of (x^2/(y^2)) is (2x(-x\frac{dy)/(dx)+y)}{y^3}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{x ^{2}}{y ^{2}})

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

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{y ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

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

Simplify

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

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

\frac{d}{d x} (\frac{sin ( x )}{2 + cos ( x )})

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

\int 30 sin^{3} (x co) s^{2} x d x

What is the derivative of (x^2/(y^2)) ?
The derivative of (x^2/(y^2)) is (2x(-x\frac{dy)/(dx)+y)}{y^3}
What is the first derivative of (x^2/(y^2)) ?
The first derivative of (x^2/(y^2)) is (2x(-x\frac{dy)/(dx)+y)}{y^3}