What is (\partial)/(\partial x)(xy^{10}+x^2+y^4) ?

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

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(\partial)/(\partial x)(xy^{10}+x^2+y^4)

\frac{\partial}{\partial x} (x y^{10} + x^{2} + y^{4})

2 x + y^{10}

Solution steps

\frac{\partial}{\partial x} (x y^{10} + x^{2} + y^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x y^{10}) = y^{10}

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

\frac{\partial}{\partial x} (y^{4}) = 0

= y^{10} + 2 x + 0

Simplify

= 2 x + y^{10}

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