What is (\partial)/(\partial v)((u^2v-v^3)^5) ?

The answer to (\partial)/(\partial v)((u^2v-v^3)^5) is 5(u^2v-v^3)^4(u^2-3v^2)

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(\partial)/(\partial v)((u^2v-v^3)^5)

\frac{\partial}{\partial v} ((u^{2} v - v^{3})^{5})

5 (u^{2} v - v^{3})^{4} (u^{2} - 3 v^{2})

Solution steps

\frac{\partial}{\partial v} ((u^{2} v - v^{3})^{5})

Treat

u

as a constant

Apply the chain rule:

5 (u^{2} v - v^{3})^{4} \frac{\partial}{\partial v} (u^{2} v - v^{3})

= 5 (u^{2} v - v^{3})^{4} \frac{\partial}{\partial v} (u^{2} v - v^{3})

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

= 5 (u^{2} v - v^{3})^{4} (u^{2} - 3 v^{2})

(- 3, 0), (0, - 3)

\frac{d}{d x} (x \cdot cos^{3} (4 x))

\frac{d}{d x} (x^{4} + e^{- x})

x \to 0 lim (2 x + 4)

x \to 0 lim (9 x - 6)

What is (\partial)/(\partial v)((u^2v-v^3)^5) ?
The answer to (\partial)/(\partial v)((u^2v-v^3)^5) is 5(u^2v-v^3)^4(u^2-3v^2)