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

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

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(\partial)/(\partial x)(yx^{y-1})

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

y x^{y - 2} (y - 1)

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

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

= y (y - 1) x^{y - 1 - 1}

Simplify

= y x^{y - 2} (y - 1)

\frac{6 x ^{2} + 8 x + 8}{x}

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

\int 3 sin^{3} (2 x co) s^{3} 2 x d x

\int (2 x - 4) (x^{2} - 4 x + 3)^{5} d x

3 x^{2} + 10 x - 26

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