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Popular >

derivative of (x^{n-1}/n)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{n} (n - 1) x^{n - 1 - 1} : \frac{x ^{n - 2} ( n - 1 )}{n}

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

Popular Examples

integral from x to 2x of y

\int_{x}^{2 x} y d y

sum from n=0 to infinity of (n^3)/(5^n)

n = 0 \sum \infty \frac{n ^{3}}{5 ^{n}}

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

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

tangent of f(x)=(4x)/(x^2-5),(3,3)tangent of

f (x) = \frac{4 x}{x ^{2} - 5}, (3, 3)

limit as x approaches 7 of (x+2)/(x-7)

x \to 7 lim (\frac{x + 2}{x - 7})

Frequently Asked Questions (FAQ)

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