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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (x^{2} + y^{2} - y^{2} x - 8)

\int 2 x - \frac{2}{x} d x

\frac{\partial}{\partial y} (x arctan (\frac{y}{z}))

x \to + (- 3) lim (2 x + 5)

g (u) = 2 u + 3 u

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