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

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

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

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

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derivative of

f (r) = \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}

\int tan^{2} (\frac{w}{2}) + sec^{2} (\frac{w}{2}) d w

\frac{d}{d x} (sin (3 x) cos (x))

\int (9 x^{2} - 7) d x

\int \frac{- 2 y - 2}{y ^{2} + y} d y

x \to 0 - lim (\frac{x}{∣ x + 1 ∣})

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