What is (\partial)/(\partial x)(2x^4+5y^4-xy+1) ?

The answer to (\partial)/(\partial x)(2x^4+5y^4-xy+1) is 8x^3-y

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(\partial)/(\partial x)(2x^4+5y^4-xy+1)

\frac{\partial}{\partial x} (2 x^{4} + 5 y^{4} - x y + 1)

8 x^{3} - y

Solution steps

\frac{\partial}{\partial x} (2 x^{4} + 5 y^{4} - x y + 1)

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^{4}) - \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (5 y^{4}) = 0

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

\frac{\partial}{\partial x} (1) = 0

= 8 x^{3} + 0 - y + 0

Simplify

= 8 x^{3} - y

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What is (\partial)/(\partial x)(2x^4+5y^4-xy+1) ?
The answer to (\partial)/(\partial x)(2x^4+5y^4-xy+1) is 8x^3-y