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Popular Calculus >

derivative of f(x)=ln(x+ln(x))

Solution

derivative of

f (x) = ln (x + ln (x))

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of-1/(1-x)

d er i v a t i v e - \frac{1}{1 - x}

(\partial)/(\partial x)(2e^yxy)

\frac{\partial}{\partial x} (2 e^{y} x y)

tangent of f(x)=-3x^{2/3},\at x=-8

t an g e n t f (x) = - 3 x^{\frac{2}{3}}, at x = - 8

limit as x approaches+0 of x^x

x \to + 0 lim (x^{x})

integral of y^{-1}

\int y^{- 1} d y

Frequently Asked Questions (FAQ)

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