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

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

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

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

2 x + y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

= 2 x + y^{2} + 0

Simplify

= 2 x + y^{2}

\int_{0}^{1} (x^{2} + 8) (e^{- x}) d x

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

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

\int_{1}^{2} (x - \frac{1}{x}) d x

\int_{2}^{5} \frac{ln ( x ^{5} )}{x} d x

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