What is (\partial)/(\partial r)(sqrt(r^2+s^2)) ?

The answer to (\partial)/(\partial r)(sqrt(r^2+s^2)) is r/(sqrt(r^2+s^2))

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(\partial)/(\partial r)(sqrt(r^2+s^2))

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

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

Solution steps

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

Treat

s

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 r ^{2} + s ^{2}} \cdot 2 r

Simplify

\frac{1}{2 r ^{2} + s ^{2}} \cdot 2 r : \frac{r}{r ^{2} + s ^{2}}

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

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

d er i v a t i v e y = (7 - 3 x^{3})^{3}

\int 16 e^{x} d x

d er i v a t i v e \frac{f ( x )}{x ^{2} + 8}

\frac{d x}{d t} = 0.3 \cdot 10 - \frac{x}{40}

What is (\partial)/(\partial r)(sqrt(r^2+s^2)) ?
The answer to (\partial)/(\partial r)(sqrt(r^2+s^2)) is r/(sqrt(r^2+s^2))