What is (\partial)/(\partial x)(x^3+2^y+x^y) ?

The answer to (\partial)/(\partial x)(x^3+2^y+x^y) is 3x^2+yx^{y-1}

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(\partial)/(\partial x)(x^3+2^y+x^y)

\frac{\partial}{\partial x} (x^{3} + 2^{y} + x^{y})

3 x^{2} + y x^{y - 1}

Solution steps

\frac{\partial}{\partial x} (x^{3} + 2^{y} + x^{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (2^{y}) + \frac{\partial}{\partial x} (x^{y})

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

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

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

= 3 x^{2} + 0 + y x^{y - 1}

Simplify

= 3 x^{2} + y x^{y - 1}

What is (\partial)/(\partial x)(x^3+2^y+x^y) ?
The answer to (\partial)/(\partial x)(x^3+2^y+x^y) is 3x^2+yx^{y-1}