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Popular >

derivative of (1-xln(1-x))

Solution

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

Solution

- ln (1 - x) - 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - ln (1 - x) - 1

Graph

Popular Examples

integral of (3x^2)/8

\int \frac{3 x ^{2}}{8} d x

integral from 1 to 25 of sqrt(x)ln(x)

\int_{1}^{25} x ln (x) d x

derivative of f(x)=(sqrt(x))/x derivative of

f (x) = \frac{x}{x}

y^{'''}-4y^{''}+4y^'=8x

y^{^{'''}} - 4 y^{^{''}} + 4 y^{^{'}} = 8 x

integral of 5x^2e^{-x}

\int 5 x^{2} e^{- x} d x

Frequently Asked Questions (FAQ)

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