What is (\partial)/(\partial v)((z)(2u^2+2v^2)^2) ?

The answer to (\partial)/(\partial v)((z)(2u^2+2v^2)^2) is 8zv(2u^2+2v^2)

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(\partial)/(\partial v)((z)(2u^2+2v^2)^2)

\frac{\partial}{\partial v} ((z) (2 u^{2} + 2 v^{2})^{2})

8 z v (2 u^{2} + 2 v^{2})

Solution steps

\frac{\partial}{\partial v} ((z) (2 u^{2} + 2 v^{2})^{2})

Treat

z, u

as constants

Take the constant out:

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

= z \frac{\partial}{\partial v} ((2 u^{2} + 2 v^{2})^{2})

Apply the chain rule:

2 (2 u^{2} + 2 v^{2}) \frac{\partial}{\partial v} (2 u^{2} + 2 v^{2})

= 2 (2 u^{2} + 2 v^{2}) \frac{\partial}{\partial v} (2 u^{2} + 2 v^{2})

\frac{\partial}{\partial v} (2 u^{2} + 2 v^{2}) = 4 v

= z \cdot 2 (2 u^{2} + 2 v^{2}) \cdot 4 v

Simplify

= 8 z v (2 u^{2} + 2 v^{2})

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What is (\partial)/(\partial v)((z)(2u^2+2v^2)^2) ?
The answer to (\partial)/(\partial v)((z)(2u^2+2v^2)^2) is 8zv(2u^2+2v^2)