en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=sqrt(x+ln(3x))

Solution

derivative of

y = x + ln (3 x)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral from 0 to (3pi)/4 of sec^4(x/3)

\int_{0}^{\frac{3 π}{4}} sec^{4} (\frac{x}{3}) d x

integral of 2rsqrt(1-r^2)

\int 2 r 1 - r^{2} d r

derivative of (x^3+3x/(x^2+1))

\frac{d}{d x} (\frac{x ^{3} + 3 x}{x ^{2} + 1})

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

integral of x\sqrt[4]{1-x^2}

Frequently Asked Questions (FAQ)

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