What is the derivative of r/(sqrt(r^2+8)) ?

The derivative of r/(sqrt(r^2+8)) is 8/((r^2+8)sqrt(r^2+8))

What is the first derivative of r/(sqrt(r^2+8)) ?

The first derivative of r/(sqrt(r^2+8)) is 8/((r^2+8)sqrt(r^2+8))

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derivative of

\frac{r}{r ^{2} + 8}

\frac{8}{( r ^{2} + 8 ) r ^{2} + 8}

Solution steps

\frac{d}{d r} (\frac{r}{r ^{2} + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d r}{d r} r ^{2} + 8 - \frac{d}{d r} ( r ^{2} + 8 ) r}{( r ^{2} + 8 ) ^{2}}

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

\frac{d}{d r} (r^{2} + 8) = \frac{r}{r ^{2} + 8}

= \frac{1 \cdot r ^{2} + 8 - \frac{r}{r ^{2} + 8} r}{( r ^{2} + 8 ) ^{2}}

Simplify

\frac{1 \cdot r ^{2} + 8 - \frac{r}{r ^{2} + 8} r}{( r ^{2} + 8 ) ^{2}} : \frac{8}{( r ^{2} + 8 ) r ^{2} + 8}

= \frac{8}{( r ^{2} + 8 ) r ^{2} + 8}

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

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What is the derivative of r/(sqrt(r^2+8)) ?
The derivative of r/(sqrt(r^2+8)) is 8/((r^2+8)sqrt(r^2+8))
What is the first derivative of r/(sqrt(r^2+8)) ?
The first derivative of r/(sqrt(r^2+8)) is 8/((r^2+8)sqrt(r^2+8))