What is (\partial)/(\partial v)(3yuxuv^3-2) ?

The answer to (\partial)/(\partial v)(3yuxuv^3-2) is 9yu^2xv^2

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(\partial)/(\partial v)(3yuxuv^3-2)

\frac{\partial}{\partial v} (3 y uxu v^{3} - 2)

9 y u^{2} x v^{2}

Solution steps

\frac{\partial}{\partial v} (3 y uxu v^{3} - 2)

Simplify

3 y uxu v^{3} - 2 : 3 y u^{2} x v^{3} - 2

= \frac{\partial}{\partial v} (3 y u^{2} x v^{3} - 2)

Treat

y, u, x

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial v} (3 y u^{2} x v^{3}) - \frac{\partial}{\partial v} (2)

\frac{\partial}{\partial v} (3 y u^{2} x v^{3}) = 9 y u^{2} x v^{2}

\frac{\partial}{\partial v} (2) = 0

= 9 y u^{2} x v^{2} - 0

Simplify

= 9 y u^{2} x v^{2}

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What is (\partial)/(\partial v)(3yuxuv^3-2) ?
The answer to (\partial)/(\partial v)(3yuxuv^3-2) is 9yu^2xv^2