What is (\partial)/(\partial x)(2x^3+xy^2+5x^2+y^2) ?

The answer to (\partial)/(\partial x)(2x^3+xy^2+5x^2+y^2) is 6x^2+10x+y^2

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(\partial)/(\partial x)(2x^3+xy^2+5x^2+y^2)

\frac{\partial}{\partial x} (2 x^{3} + x y^{2} + 5 x^{2} + y^{2})

6 x^{2} + 10 x + y^{2}

Solution steps

\frac{\partial}{\partial x} (2 x^{3} + x y^{2} + 5 x^{2} + y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{3}) + \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (5 x^{2}) + \frac{\partial}{\partial x} (y^{2})

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

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

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

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

= 6 x^{2} + y^{2} + 10 x + 0

Simplify

= 6 x^{2} + 10 x + y^{2}

What is (\partial)/(\partial x)(2x^3+xy^2+5x^2+y^2) ?
The answer to (\partial)/(\partial x)(2x^3+xy^2+5x^2+y^2) is 6x^2+10x+y^2