en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=sqrt(x+\sqrt{x)}

Solution

derivative of

f (x) = x + x

Solution

\frac{2 x + 1}{4 x x + x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x + x} (1 + \frac{1}{2 x}) : \frac{2 x + 1}{4 x x + x}

= \frac{2 x + 1}{4 x x + x}

Popular Examples

integral of 1/(x-2x^{3/4)-8sqrt(x)}

\int \frac{1}{x - 2 x ^{\frac{3}{4}} - 8 x} d x

sum from n=0 to infinity of (5+n)/(10^n)

n = 0 \sum \infty \frac{5 + n}{1 0 ^{n}}

integral of ((csc(x)+cot(x))/(sin(x)))

\int (\frac{csc ( x ) + cot ( x )}{sin ( x )}) d x

integral of x^{4035}e^{x^{2018}}

\int x^{4035} e^{x^{2018}} d x

limit as x approaches 1 of xarcsin(x/2)

x \to 1 lim (x arcsin (\frac{x}{2}))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(x+\sqrt{x)} ?
The derivative of f(x)=sqrt(x+\sqrt{x)} is (2sqrt(x)+1)/(4sqrt(x)\sqrt{x+\sqrt{x)}}
What is the first derivative of f(x)=sqrt(x+\sqrt{x)} ?
The first derivative of f(x)=sqrt(x+\sqrt{x)} is (2sqrt(x)+1)/(4sqrt(x)\sqrt{x+\sqrt{x)}}