en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of sqrt(ln(3x))

Solution

\frac{d}{d x} (ln (3 x))

Solution

\frac{1}{2 x ln ( 3 x )}

Solution steps

\frac{d}{d x} (ln (3 x))

Apply the chain rule:

\frac{1}{2 ln ( 3 x )} \frac{d}{d x} (ln (3 x))

= \frac{1}{2 ln ( 3 x )} \frac{d}{d x} (ln (3 x))

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= \frac{1}{2 ln ( 3 x )} \cdot \frac{1}{x}

Simplify

\frac{1}{2 ln ( 3 x )} \cdot \frac{1}{x} : \frac{1}{2 x ln ( 3 x )}

= \frac{1}{2 x ln ( 3 x )}

Graph

Popular Examples

sum from n=1 to infinity of e^{-5n}

n = 1 \sum \infty e^{- 5 n}

(\partial)/(\partial x)(ycos(2x))

\frac{\partial}{\partial x} (y cos (2 x))

derivative of (x-9xsqrt(x))/(sqrt(x))

d er i v a t i v e \frac{x - 9 x x}{x}

y(2x+x^2cot(x))dx+x^2(1+y)dy=0

y (2 x + x^{2} cot (x)) d x + x^{2} (1 + y) d y = 0

derivative of e^{\sqrt[3]{x}}

d er i v a t i v e e^{3 x}

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(ln(3x)) ?
The derivative of sqrt(ln(3x)) is 1/(2xsqrt(ln(3x)))
What is the first derivative of sqrt(ln(3x)) ?
The first derivative of sqrt(ln(3x)) is 1/(2xsqrt(ln(3x)))