What is the derivative of r/(sqrt(r^2+5)) ?

The derivative of r/(sqrt(r^2+5)) is 5/((r^2+5)sqrt(r^2+5))

What is the first derivative of r/(sqrt(r^2+5)) ?

The first derivative of r/(sqrt(r^2+5)) is 5/((r^2+5)sqrt(r^2+5))

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derivative of

\frac{r}{r ^{2} + 5}

\frac{5}{( r ^{2} + 5 ) r ^{2} + 5}

Solution steps

\frac{d}{d r} (\frac{r}{r ^{2} + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d r}{d r} r ^{2} + 5 - \frac{d}{d r} ( r ^{2} + 5 ) r}{( r ^{2} + 5 ) ^{2}}

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

\frac{d}{d r} (r^{2} + 5) = \frac{r}{r ^{2} + 5}

= \frac{1 \cdot r ^{2} + 5 - \frac{r}{r ^{2} + 5} r}{( r ^{2} + 5 ) ^{2}}

Simplify

\frac{1 \cdot r ^{2} + 5 - \frac{r}{r ^{2} + 5} r}{( r ^{2} + 5 ) ^{2}} : \frac{5}{( r ^{2} + 5 ) r ^{2} + 5}

= \frac{5}{( r ^{2} + 5 ) r ^{2} + 5}

\frac{d}{d x} (\frac{110}{x ^{12}})

\frac{d}{d x} (5 tan (x))

\int tan (5 x) (sec (5 x))^{2} d x

\frac{d}{d x} (sin^{3} (4 x))

\int \frac{1}{x ( x + 0 )} d x

What is the derivative of r/(sqrt(r^2+5)) ?
The derivative of r/(sqrt(r^2+5)) is 5/((r^2+5)sqrt(r^2+5))
What is the first derivative of r/(sqrt(r^2+5)) ?
The first derivative of r/(sqrt(r^2+5)) is 5/((r^2+5)sqrt(r^2+5))