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(sqrt(x+2))

Solution

derivative of

y = ln (x + 2)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{x + 2} \cdot \frac{1}{2 x + 2}

Simplify

\frac{1}{x + 2} \cdot \frac{1}{2 x + 2} : \frac{1}{2 ( x + 2 )}

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

Popular Examples

slope ofintercept (1/2 ,-1/2),(5,-1/2)slope intercept

(\frac{1}{2}, - \frac{1}{2}), (5, - \frac{1}{2})

integral of (12x^2-6x+2)

\int (12 x^{2} - 6 x + 2) d x

(\partial)/(\partial y)(sin(xy)+xycos(xy))

\frac{\partial}{\partial y} (sin (x y) + x y cos (x y))

(\partial)/(\partial x)(x(x^2-3y^2))

\frac{\partial}{\partial x} (x (x^{2} - 3 y^{2}))

limit as x approaches 0 of (e^{2x-1})/(tan(x))

x \to 0 lim (\frac{e ^{2 x - 1}}{tan ( x )})

Frequently Asked Questions (FAQ)

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