What is (\partial)/(\partial s)(4s^3t^2+2st) ?

The answer to (\partial)/(\partial s)(4s^3t^2+2st) is 12t^2s^2+2t

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(\partial)/(\partial s)(4s^3t^2+2st)

\frac{\partial}{\partial s} (4 s^{3} t^{2} + 2 s t)

12 t^{2} s^{2} + 2 t

Solution steps

\frac{\partial}{\partial s} (4 s^{3} t^{2} + 2 s t)

Treat

t

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial s} (4 s^{3} t^{2}) + \frac{\partial}{\partial s} (2 s t)

\frac{\partial}{\partial s} (4 s^{3} t^{2}) = 12 t^{2} s^{2}

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

= 12 t^{2} s^{2} + 2 t

8 y^{^{''}} - 32 y = 0

cos (\frac{π}{4})

\frac{\partial}{\partial x} (ln (t^{2} + x^{2}))

f (x) = 18 x

\int \frac{11}{x ^{3} - 125} d x

What is (\partial)/(\partial s)(4s^3t^2+2st) ?
The answer to (\partial)/(\partial s)(4s^3t^2+2st) is 12t^2s^2+2t