What is the derivative of nx^{n-1} ?

The derivative of nx^{n-1} is nx^{n-2}(n-1)

What is the first derivative of nx^{n-1} ?

The first derivative of nx^{n-1} is nx^{n-2}(n-1)

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\frac{d}{d x} (n x^{n - 1})

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

Solution steps

\frac{d}{d x} (n x^{n - 1})

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

\int - x e^{- 4 x} d x

d er i v a t i v e f (x) = x^{3} - 12 x^{2} + 48 x

y^{^{''}} + 2 y^{^{'}} - 8 y = x e^{- x} + e^{- x}

\frac{\partial}{\partial x} (- u (x, y) cos (k x) sin (k y))

\frac{d}{d x} (x^{\frac{2}{3}} - a^{\frac{2}{3}})

What is the derivative of nx^{n-1} ?
The derivative of nx^{n-1} is nx^{n-2}(n-1)
What is the first derivative of nx^{n-1} ?
The first derivative of nx^{n-1} is nx^{n-2}(n-1)