en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of x^n(ln(x)^2)

Solution

\frac{d}{d x} (x^{n} (ln (x))^{2})

Solution

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

Solution steps

\frac{d}{d x} (x^{n} (ln (x))^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{n}, g = (ln (x))^{2}

= \frac{d}{d x} (x^{n}) (ln (x))^{2} + \frac{d}{d x} ((ln (x))^{2}) x^{n}

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

\frac{d}{d x} ((ln (x))^{2}) = \frac{2 ln ( x )}{x}

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

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

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

Graph

Popular Examples

derivative of f(x)=(9-xe^x)/(x+e^x)derivative of

f (x) = \frac{9 - x e ^{x}}{x + e ^{x}}

derivative of (5x-2^3)

\frac{d}{d x} ((5 x - 2)^{3})

derivative of sin^2(pi-x)

\frac{d}{d x} (sin^{2} (π - x))

(dy)/(dt)=(3t^2+te^{-t}+1)/(2y-4)

\frac{d y}{d t} = \frac{3 t ^{2} + t e ^{- t} + 1}{2 y - 4}

integral of a/(x^2)

\int \frac{a}{x ^{2}} d x

Frequently Asked Questions (FAQ)

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