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

The answer to (\partial)/(\partial x)((x^2+y^2)^3) is 6x(x^2+y^2)^2

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

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

6 x (x^{2} + y^{2})^{2}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 6 x (x^{2} + y^{2})^{2}

\frac{\partial}{\partial x} (f (x, y) x (x, y))

\frac{d y}{d x} = 8 y

f (x) = (\frac{2}{x - 2}), at x = 4

\int_{0}^{l n (3)} \frac{3}{e ^{x} + 2} d x

(x - 2) \frac{d y}{d x} - y = 3

What is (\partial)/(\partial x)((x^2+y^2)^3) ?
The answer to (\partial)/(\partial x)((x^2+y^2)^3) is 6x(x^2+y^2)^2