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

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

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

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

y x^{y - 1}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= y x^{y - 1} + 0

Simplify

= y x^{y - 1}

\frac{4}{x}

\int (3 x^{2} + 6 x) (x^{3} + 3 x^{2} + 1)^{\frac{2}{3}} d x

\int \frac{x + 3}{x ^{2} + 4 x + 5} d x

ln (7 x^{2} + 3 y^{2})

\int cot^{3} (3 x) csc^{5} (3 x) d x

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