en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=ln(x+sqrt(x^2-12))

Solution

derivative of

f (x) = ln (x + x^{2} - 12)

Solution

\frac{1}{x ^{2} - 12}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 12))

Apply the chain rule:

\frac{1}{x + x ^{2} - 12} \frac{d}{d x} (x + x^{2} - 12)

= \frac{1}{x + x ^{2} - 12} \frac{d}{d x} (x + x^{2} - 12)

\frac{d}{d x} (x + x^{2} - 12) = 1 + \frac{x}{x ^{2} - 12}

= \frac{1}{x + x ^{2} - 12} (1 + \frac{x}{x ^{2} - 12})

Simplify

\frac{1}{x + x ^{2} - 12} (1 + \frac{x}{x ^{2} - 12}) : \frac{1}{x ^{2} - 12}

= \frac{1}{x ^{2} - 12}

Popular Examples

tangent of y=(-2x)/((x^2+1))tangent of

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

limit as x approaches 0 of x/0

x \to 0 lim (\frac{x}{0})

limit as x approaches-2 of x^2+3x-7

x \to - 2 lim (x^{2} + 3 x - 7)

(\partial)/(\partial x)(-xyz^2+1)

\frac{\partial}{\partial x} (- x y z^{2} + 1)

f(x)=-e^xx+3e^x

f (x) = - e^{x} x + 3 e^{x}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=ln(x+sqrt(x^2-12)) ?
The derivative of f(x)=ln(x+sqrt(x^2-12)) is 1/(sqrt(x^2-12))
What is the first derivative of f(x)=ln(x+sqrt(x^2-12)) ?
The first derivative of f(x)=ln(x+sqrt(x^2-12)) is 1/(sqrt(x^2-12))