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

The answer to (\partial)/(\partial u)((u^2v-v^3)^5) is 10uv(u^2v-v^3)^4

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

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

10 uv (u^{2} v - v^{3})^{4}

Solution steps

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

Treat

v

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 10 uv (u^{2} v - v^{3})^{4}

\int x y sin (z) d z

y = x^{- \frac{1}{7}}, (1, 1)

\frac{\partial}{\partial x} (x^{2} + 2 x y + 2 y^{2} - 6 x + 6 y)

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 3) x^{2})

\frac{d}{d x} (- 2 x^{- 3})

What is (\partial)/(\partial u)((u^2v-v^3)^5) ?
The answer to (\partial)/(\partial u)((u^2v-v^3)^5) is 10uv(u^2v-v^3)^4