What is the derivative of r/(sqrt(r^2+9)) ?

The derivative of r/(sqrt(r^2+9)) is 9/((r^2+9)sqrt(r^2+9))

What is the first derivative of r/(sqrt(r^2+9)) ?

The first derivative of r/(sqrt(r^2+9)) is 9/((r^2+9)sqrt(r^2+9))

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derivative of

\frac{r}{r ^{2} + 9}

\frac{9}{( r ^{2} + 9 ) r ^{2} + 9}

Solution steps

\frac{d}{d r} (\frac{r}{r ^{2} + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d r}{d r} r ^{2} + 9 - \frac{d}{d r} ( r ^{2} + 9 ) r}{( r ^{2} + 9 ) ^{2}}

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

\frac{d}{d r} (r^{2} + 9) = \frac{r}{r ^{2} + 9}

= \frac{1 \cdot r ^{2} + 9 - \frac{r}{r ^{2} + 9} r}{( r ^{2} + 9 ) ^{2}}

Simplify

\frac{1 \cdot r ^{2} + 9 - \frac{r}{r ^{2} + 9} r}{( r ^{2} + 9 ) ^{2}} : \frac{9}{( r ^{2} + 9 ) r ^{2} + 9}

= \frac{9}{( r ^{2} + 9 ) r ^{2} + 9}

x \to 0 lim (\frac{8}{x ^{2} + x} - \frac{8}{x})

x \to 1 lim (\frac{1}{a x + 2})

\int_{- 5}^{1} ∣ x + 2 ∣ d x

\frac{\partial}{\partial y} (- 4 y)

What is the derivative of r/(sqrt(r^2+9)) ?
The derivative of r/(sqrt(r^2+9)) is 9/((r^2+9)sqrt(r^2+9))
What is the first derivative of r/(sqrt(r^2+9)) ?
The first derivative of r/(sqrt(r^2+9)) is 9/((r^2+9)sqrt(r^2+9))