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

The answer to (\partial)/(\partial s)(t+3t^3sin(s)) is 3t^3cos(s)

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(\partial)/(\partial s)(t+3t^3sin(s))

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

3 t^{3} cos (s)

Solution steps

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

Treat

t

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial s} (t) = 0

\frac{\partial}{\partial s} (3 t^{3} sin (s)) = 3 t^{3} cos (s)

= 0 + 3 t^{3} cos (s)

Simplify

= 3 t^{3} cos (s)

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