What is (\partial)/(\partial s)(3sqrt(s^2+t^2)) ?

The answer to (\partial)/(\partial s)(3sqrt(s^2+t^2)) is (3s)/(sqrt(s^2+t^2))

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(\partial)/(\partial s)(3sqrt(s^2+t^2))

\frac{\partial}{\partial s} (3 s^{2} + t^{2})

\frac{3 s}{s ^{2} + t ^{2}}

Solution steps

\frac{\partial}{\partial s} (3 s^{2} + t^{2})

Treat

t

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{\partial}{\partial s} (s^{2} + t^{2})

Apply the chain rule:

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

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

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

= 3 \cdot \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 s

Simplify

3 \cdot \frac{1}{2 s ^{2} + t ^{2}} \cdot 2 s : \frac{3 s}{s ^{2} + t ^{2}}

= \frac{3 s}{s ^{2} + t ^{2}}

\frac{d y}{d x} = x - y, y (0) = 2

x \to 0 lim (ln (\frac{1}{x ^{2}}))

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

\int_{0}^{N} e^{- s t} cos (3 t) d t

y = 4 x - 3 x^{2}, (2, - 4)

What is (\partial)/(\partial s)(3sqrt(s^2+t^2)) ?
The answer to (\partial)/(\partial s)(3sqrt(s^2+t^2)) is (3s)/(sqrt(s^2+t^2))