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

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

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

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

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

Solution steps

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

Treat

r

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

n = 5 \sum \infty tan (\frac{1}{n})

\frac{d}{d x} (2 x - 2 sin (x))

f (x) = x^{4} + 8 x^{2} - x, (1, 8)

\frac{d}{d x} (y e^{x y})

\int_{0}^{2} \frac{1}{2 - x} d x

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