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

The answer to (\partial)/(\partial x)(2x^4+5y^2+xy) is 8x^3+y

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

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

8 x^{3} + y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{4}) = 8 x^{3}

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

= 8 x^{3} + 0 + y

Simplify

= 8 x^{3} + y

What is (\partial)/(\partial x)(2x^4+5y^2+xy) ?
The answer to (\partial)/(\partial x)(2x^4+5y^2+xy) is 8x^3+y