What is (\partial)/(\partial x)(x^4+5x^2y) ?

The answer to (\partial)/(\partial x)(x^4+5x^2y) is 4x^3+10yx

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(\partial)/(\partial x)(x^4+5x^2y)

\frac{\partial}{\partial x} (x^{4} + 5 x^{2} y)

4 x^{3} + 10 y x

Solution steps

\frac{\partial}{\partial x} (x^{4} + 5 x^{2} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{4}) + \frac{\partial}{\partial x} (5 x^{2} y)

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} + 10 y x

What is (\partial)/(\partial x)(x^4+5x^2y) ?
The answer to (\partial)/(\partial x)(x^4+5x^2y) is 4x^3+10yx