What is the derivative of r/(sqrt(r^2+4)) ?

The derivative of r/(sqrt(r^2+4)) is 4/((r^2+4)sqrt(r^2+4))

What is the first derivative of r/(sqrt(r^2+4)) ?

The first derivative of r/(sqrt(r^2+4)) is 4/((r^2+4)sqrt(r^2+4))

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derivative of

\frac{r}{r ^{2} + 4}

\frac{4}{( r ^{2} + 4 ) r ^{2} + 4}

Solution steps

\frac{d}{d r} (\frac{r}{r ^{2} + 4})

Apply the Quotient Rule:

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

= \frac{\frac{d r}{d r} r ^{2} + 4 - \frac{d}{d r} ( r ^{2} + 4 ) r}{( r ^{2} + 4 ) ^{2}}

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

\frac{d}{d r} (r^{2} + 4) = \frac{r}{r ^{2} + 4}

= \frac{1 \cdot r ^{2} + 4 - \frac{r}{r ^{2} + 4} r}{( r ^{2} + 4 ) ^{2}}

Simplify

\frac{1 \cdot r ^{2} + 4 - \frac{r}{r ^{2} + 4} r}{( r ^{2} + 4 ) ^{2}} : \frac{4}{( r ^{2} + 4 ) r ^{2} + 4}

= \frac{4}{( r ^{2} + 4 ) r ^{2} + 4}

x \frac{d y}{d x} = x^{3} + 4 x^{3} y

n = 1 \sum \infty \frac{n 5 ^{n}}{n !}

5 tan (x)

x (x - 14)

x \to 0 lim (e^{- x})

What is the derivative of r/(sqrt(r^2+4)) ?
The derivative of r/(sqrt(r^2+4)) is 4/((r^2+4)sqrt(r^2+4))
What is the first derivative of r/(sqrt(r^2+4)) ?
The first derivative of r/(sqrt(r^2+4)) is 4/((r^2+4)sqrt(r^2+4))