en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=ln(x+sqrt(x^2-6))

Solution

derivative of

y = ln (x + x^{2} - 6)

Solution

\frac{1}{x ^{2} - 6}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 6))

Apply the chain rule:

\frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

= \frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

\frac{d}{d x} (x + x^{2} - 6) = 1 + \frac{x}{x ^{2} - 6}

= \frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6})

Simplify

\frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6}) : \frac{1}{x ^{2} - 6}

= \frac{1}{x ^{2} - 6}

Popular Examples

d/(da)(csc(a)tan(a)cos(a)-csc^2(a))

\frac{d}{d a} (csc (a) tan (a) cos (a) - csc^{2} (a))

limit as x approaches 0 of ln(x^2+1)

x \to 0 lim (ln (x^{2} + 1))

y^{''}+3y^'-4y=0

y^{^{''}} + 3 y^{^{'}} - 4 y = 0

integral of (cos(x))(tan(x))

\int (cos (x)) (tan (x)) d x

limit as x approaches 3-of (x-3)/(x-3)

x \to 3 - lim (\frac{x - 3}{x - 3})

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(x+sqrt(x^2-6)) ?
The derivative of y=ln(x+sqrt(x^2-6)) is 1/(sqrt(x^2-6))
What is the first derivative of y=ln(x+sqrt(x^2-6)) ?
The first derivative of y=ln(x+sqrt(x^2-6)) is 1/(sqrt(x^2-6))