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

The answer to (\partial)/(\partial x)((x^3+2y^2)^3) is 9x^2(x^3+2y^2)^2

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

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

9 x^{2} (x^{3} + 2 y^{2})^{2}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 9 x^{2} (x^{3} + 2 y^{2})^{2}

x \to - \infty lim (4^{x} + 5)

\int_{1}^{4} \frac{1}{4 x + 7} d x

\frac{( x ^{2} + x ) ( 2 x + 1 )}{4 x}

x \to - 4 - lim (\frac{x + 2}{x + 4})

\int_{- 3}^{3} 2 - ∣ x ∣ d x

What is (\partial)/(\partial x)((x^3+2y^2)^3) ?
The answer to (\partial)/(\partial x)((x^3+2y^2)^3) is 9x^2(x^3+2y^2)^2