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)ln(x)

Solution

derivative of

f (x) = x ln (x)

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x)

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 2 of x^2-6x

x \to 2 lim (x^{2} - 6 x)

y^{''}+5y^'+4y=-18te^{4t}

y^{^{''}} + 5 y^{^{'}} + 4 y = - 18 t e^{4 t}

derivative of xe^{-sin(x}-x)

\frac{d}{d x} (x e^{- s i n (x)} - x)

limit as x approaches 2 of sqrt(2.1-1)+3

x \to 2 lim (2.1 - 1 + 3)

tangent of f(x)=(x^2-12)(2x-9)tangent of

f (x) = (x^{2} - 12) (2 x - 9)

Frequently Asked Questions (FAQ)

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