What is the derivative of r/(sqrt(r^2+1)) ?

The derivative of r/(sqrt(r^2+1)) is 1/((r^2+1)sqrt(r^2+1))

What is the first derivative of r/(sqrt(r^2+1)) ?

The first derivative of r/(sqrt(r^2+1)) is 1/((r^2+1)sqrt(r^2+1))

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derivative of

\frac{r}{r ^{2} + 1}

\frac{1}{( r ^{2} + 1 ) r ^{2} + 1}

Solution steps

\frac{d}{d r} (\frac{r}{r ^{2} + 1})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int (- 0.5 x + 450) d x

\frac{d y}{d x} = 4 x - 5

x \to 0 lim ((x)^{t a n (x)})

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

y = 7 x + 1, (5, 6)

What is the derivative of r/(sqrt(r^2+1)) ?
The derivative of r/(sqrt(r^2+1)) is 1/((r^2+1)sqrt(r^2+1))
What is the first derivative of r/(sqrt(r^2+1)) ?
The first derivative of r/(sqrt(r^2+1)) is 1/((r^2+1)sqrt(r^2+1))