What is (\partial)/(\partial x)((x^3+y^2)^5) ?

The answer to (\partial)/(\partial x)((x^3+y^2)^5) is 15x^2(x^3+y^2)^4

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(\partial)/(\partial x)((x^3+y^2)^5)

\frac{\partial}{\partial x} ((x^{3} + y^{2})^{5})

15 x^{2} (x^{3} + y^{2})^{4}

Solution steps

\frac{\partial}{\partial x} ((x^{3} + y^{2})^{5})

Treat

y

as a constant

Apply the chain rule:

5 (x^{3} + y^{2})^{4} \frac{\partial}{\partial x} (x^{3} + y^{2})

= 5 (x^{3} + y^{2})^{4} \frac{\partial}{\partial x} (x^{3} + y^{2})

\frac{\partial}{\partial x} (x^{3} + y^{2}) = 3 x^{2}

= 5 (x^{3} + y^{2})^{4} \cdot 3 x^{2}

Simplify

= 15 x^{2} (x^{3} + y^{2})^{4}

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x \to 2 lim (x^{3} - x^{2} + 2 x)

\frac{1}{2 s ^{2} + 10 s + 12}

\int x^{\frac{1}{3}} d x

What is (\partial)/(\partial x)((x^3+y^2)^5) ?
The answer to (\partial)/(\partial x)((x^3+y^2)^5) is 15x^2(x^3+y^2)^4