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

The answer to (\partial)/(\partial x)((x^2+y^2)^5) is 10x(x^2+y^2)^4

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

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

10 x (x^{2} + y^{2})^{4}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 10 x (x^{2} + y^{2})^{4}

y = x^{2} - x + 9

\frac{d y}{( 5 - 3 y ) ^{2}} = \frac{d x}{2 ( 4 - x )}

e^{- 0.75 t} cos (4 t)

f (x) = \frac{1}{2} x^{2}, at x = 2

\int \frac{1 - x ^{2}}{1 - x} d x

What is (\partial)/(\partial x)((x^2+y^2)^5) ?
The answer to (\partial)/(\partial x)((x^2+y^2)^5) is 10x(x^2+y^2)^4