What is the derivative of r/(sqrt(r^2+7)) ?

The derivative of r/(sqrt(r^2+7)) is 7/((r^2+7)sqrt(r^2+7))

What is the first derivative of r/(sqrt(r^2+7)) ?

The first derivative of r/(sqrt(r^2+7)) is 7/((r^2+7)sqrt(r^2+7))

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derivative of

\frac{r}{r ^{2} + 7}

\frac{7}{( r ^{2} + 7 ) r ^{2} + 7}

Solution steps

\frac{d}{d r} (\frac{r}{r ^{2} + 7})

Apply the Quotient Rule:

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

= \frac{\frac{d r}{d r} r ^{2} + 7 - \frac{d}{d r} ( r ^{2} + 7 ) r}{( r ^{2} + 7 ) ^{2}}

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

\frac{d}{d r} (r^{2} + 7) = \frac{r}{r ^{2} + 7}

= \frac{1 \cdot r ^{2} + 7 - \frac{r}{r ^{2} + 7} r}{( r ^{2} + 7 ) ^{2}}

Simplify

\frac{1 \cdot r ^{2} + 7 - \frac{r}{r ^{2} + 7} r}{( r ^{2} + 7 ) ^{2}} : \frac{7}{( r ^{2} + 7 ) r ^{2} + 7}

= \frac{7}{( r ^{2} + 7 ) r ^{2} + 7}

f (x) = \frac{4 x ^{3} + 2 x + 5}{x}

f (x) = \frac{5}{( x + 2 ) ^{2}}

\frac{d}{d x} (9 (x^{3} - x)^{4})

\int \frac{x}{( x ^{2} + a ^{2} ) ^{\frac{3}{2}}} d x

y^{^{''}} - 6 y^{^{'}} + 12 y = sin (2 x)

What is the derivative of r/(sqrt(r^2+7)) ?
The derivative of r/(sqrt(r^2+7)) is 7/((r^2+7)sqrt(r^2+7))
What is the first derivative of r/(sqrt(r^2+7)) ?
The first derivative of r/(sqrt(r^2+7)) is 7/((r^2+7)sqrt(r^2+7))