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

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

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

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

y x^{y - 1}

Solution steps

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

Treat

y

as a constant

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= y x^{y - 1}

\int - e^{2 x} x d x

\frac{\partial}{\partial x} (y^{6} cos (3 x))

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

f (x) = 3 x^{2} - 4 x, at x = - 1

\frac{d}{d y} (x - 2 y)

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