What is (\partial)/(\partial x)(x^2(1+y^2)) ?

The answer to (\partial)/(\partial x)(x^2(1+y^2)) is 2x(1+y^2)

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(\partial)/(\partial x)(x^2(1+y^2))

\frac{\partial}{\partial x} (x^{2} (1 + y^{2}))

2 x (1 + y^{2})

Solution steps

\frac{\partial}{\partial x} (x^{2} (1 + y^{2}))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= (1 + y^{2}) \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= (1 + y^{2}) \cdot 2 x^{2 - 1}

Simplify

= 2 x (1 + y^{2})

What is (\partial)/(\partial x)(x^2(1+y^2)) ?
The answer to (\partial)/(\partial x)(x^2(1+y^2)) is 2x(1+y^2)