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

The answer to (\partial)/(\partial x)(5x^4+2xy+1) is 20x^3+2y

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

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

20 x^{3} + 2 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 x^{4}) = 20 x^{3}

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

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

= 20 x^{3} + 2 y + 0

Simplify

= 20 x^{3} + 2 y

What is (\partial)/(\partial x)(5x^4+2xy+1) ?
The answer to (\partial)/(\partial x)(5x^4+2xy+1) is 20x^3+2y