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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

\int e^{4 x - 9} d x

\frac{d}{d x} (\frac{3}{e ^{x} + e ^{- x}})

\frac{d}{d x} (\frac{2}{x ^{3} + 1})

y - x y^{^{'}} = a (1 + x^{2} y^{^{'}})

x \to 3 lim (\frac{2 x - 9}{x - 3})

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