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Popular >

derivative of x(ln(x-1))

Solution

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

Solution

ln (x)

Solution steps

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

Apply the Product Rule:

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

f = x, g = ln (x) - 1

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

\frac{d x}{d x} = 1

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

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

Simplify

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

= ln (x)

Popular Examples

integral from 0 to 3/4 of 1/(9+16x^2)

\int_{0}^{\frac{3}{4}} \frac{1}{9 + 16 x ^{2}} d x

derivative of 1/(sqrt(2pi)e^{-(x^2)/2})

\frac{d}{d x} (\frac{1}{2 π} e^{- \frac{x ^{2}}{2}})

derivative of Ax^2e^x+Bxe^x+Ce^x

\frac{d}{d x} (A x^{2} e^{x} + B x e^{x} + C e^{x})

sum from n=1 to infinity of ((n+1))/(n!)

n = 1 \sum \infty \frac{( n + 1 )}{n !}

integral of (y^3)/2

\int \frac{y ^{3}}{2} d y

Frequently Asked Questions (FAQ)

What is the derivative of x(ln(x-1)) ?
The derivative of x(ln(x-1)) is ln(x)
What is the first derivative of x(ln(x-1)) ?
The first derivative of x(ln(x-1)) is ln(x)