What is (\partial)/(\partial x)(x^5+xy^7+4) ?

The answer to (\partial)/(\partial x)(x^5+xy^7+4) is 5x^4+y^7

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(\partial)/(\partial x)(x^5+xy^7+4)

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 4)

5 x^{4} + y^{7}

Solution steps

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 4)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{5}) + \frac{\partial}{\partial x} (x y^{7}) + \frac{\partial}{\partial x} (4)

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

\frac{\partial}{\partial x} (x y^{7}) = y^{7}

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

= 5 x^{4} + y^{7} + 0

Simplify

= 5 x^{4} + y^{7}

What is (\partial)/(\partial x)(x^5+xy^7+4) ?
The answer to (\partial)/(\partial x)(x^5+xy^7+4) is 5x^4+y^7