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

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

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

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

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{a ^{2} x}{b ^{2} y})

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

= - \frac{a ^{2}}{b ^{2}} \cdot \frac{\frac{d x}{d x} y - \frac{d y}{d x} x}{y ^{2}}

\frac{d x}{d x} = 1

= - \frac{a ^{2}}{b ^{2}} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}}

Simplify

- \frac{a ^{2}}{b ^{2}} \cdot \frac{1 \cdot y - \frac{d y}{d x} x}{y ^{2}} : - \frac{a ^{2} ( y - x \frac{d y}{d x} )}{b ^{2} y ^{2}}

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

\frac{d}{d x} (e^{a x^{2}})

\int_{0}^{9} π y^{2} d y

\frac{\partial}{\partial x} (x + \frac{1}{y})

\frac{( y ^{4} - x ^{2} ) d y}{d x} = - x y

\int \frac{9 + t + t ^{2}}{t} d t

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