en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(xsqrt(x^2-5))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{x x ^{2} - 5} \frac{d}{d x} (x x^{2} - 5)

= \frac{1}{x x ^{2} - 5} \frac{d}{d x} (x x^{2} - 5)

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

= \frac{1}{x x ^{2} - 5} \cdot \frac{2 x ^{2} - 5}{x ^{2} - 5}

Simplify

\frac{1}{x x ^{2} - 5} \cdot \frac{2 x ^{2} - 5}{x ^{2} - 5} : \frac{2 x ^{2} - 5}{x ( x ^{2} - 5 )}

= \frac{2 x ^{2} - 5}{x ( x ^{2} - 5 )}

Graph

Popular Examples

sum from n=0 to infinity of (x^n)/(4^n)

n = 0 \sum \infty \frac{x ^{n}}{4 ^{n}}

tangent of 2x^2,\at 2 tangent of

2 x^{2}, at 2

derivative of xe^{2x-y^2}

\frac{d}{d x} (x e^{2 x - y^{2}})

\frac{d y}{d x} - y = x

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

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(xsqrt(x^2-5)) ?
The derivative of ln(xsqrt(x^2-5)) is (2x^2-5)/(x(x^2-5))
What is the first derivative of ln(xsqrt(x^2-5)) ?
The first derivative of ln(xsqrt(x^2-5)) is (2x^2-5)/(x(x^2-5))