What is the derivative of r/(sqrt(r^2+6)) ?

The derivative of r/(sqrt(r^2+6)) is 6/((r^2+6)sqrt(r^2+6))

What is the first derivative of r/(sqrt(r^2+6)) ?

The first derivative of r/(sqrt(r^2+6)) is 6/((r^2+6)sqrt(r^2+6))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{r}{r ^{2} + 6}

\frac{6}{( r ^{2} + 6 ) r ^{2} + 6}

Solution steps

\frac{d}{d r} (\frac{r}{r ^{2} + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d r}{d r} r ^{2} + 6 - \frac{d}{d r} ( r ^{2} + 6 ) r}{( r ^{2} + 6 ) ^{2}}

\frac{d r}{d r} = 1

\frac{d}{d r} (r^{2} + 6) = \frac{r}{r ^{2} + 6}

= \frac{1 \cdot r ^{2} + 6 - \frac{r}{r ^{2} + 6} r}{( r ^{2} + 6 ) ^{2}}

Simplify

\frac{1 \cdot r ^{2} + 6 - \frac{r}{r ^{2} + 6} r}{( r ^{2} + 6 ) ^{2}} : \frac{6}{( r ^{2} + 6 ) r ^{2} + 6}

= \frac{6}{( r ^{2} + 6 ) r ^{2} + 6}

\frac{d}{d x} (e^{\frac{9}{x}})

\int \frac{1}{( 5 x ^{2} + x )} d x

\frac{d y}{d x} = 2 cos (5 x)

f (x) = 4 x + 5

What is the derivative of r/(sqrt(r^2+6)) ?
The derivative of r/(sqrt(r^2+6)) is 6/((r^2+6)sqrt(r^2+6))
What is the first derivative of r/(sqrt(r^2+6)) ?
The first derivative of r/(sqrt(r^2+6)) is 6/((r^2+6)sqrt(r^2+6))