What is (\partial)/(\partial x)((x^2+y^2)^6) ?

The answer to (\partial)/(\partial x)((x^2+y^2)^6) is 12x(x^2+y^2)^5

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(\partial)/(\partial x)((x^2+y^2)^6)

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

12 x (x^{2} + y^{2})^{5}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

= 6 (x^{2} + y^{2})^{5} \frac{\partial}{\partial x} (x^{2} + y^{2})

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

= 6 (x^{2} + y^{2})^{5} \cdot 2 x

Simplify

= 12 x (x^{2} + y^{2})^{5}

x \to 5 lim (3)

\frac{x d y}{d x} - y = 3 x^{4}

y^{^{''}} - 6 y^{^{'}} + 25 y = e^{t}

\int x^{3} arctan (x) d x

\frac{d}{d θ} (θ sin (θ))

What is (\partial)/(\partial x)((x^2+y^2)^6) ?
The answer to (\partial)/(\partial x)((x^2+y^2)^6) is 12x(x^2+y^2)^5