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

The answer to (\partial)/(\partial x)(x^5+4^y+x^y) is 5x^4+yx^{y-1}

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

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

5 x^{4} + y x^{y - 1}

Solution steps

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

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

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

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

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

= 5 x^{4} + 0 + y x^{y - 1}

Simplify

= 5 x^{4} + y x^{y - 1}

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What is (\partial)/(\partial x)(x^5+4^y+x^y) ?
The answer to (\partial)/(\partial x)(x^5+4^y+x^y) is 5x^4+yx^{y-1}