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Popular >

derivative of xln(1-x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

limit as n approaches infinity of 2^n

n \to \infty lim (2^{n})

(\partial)/(\partial x)(e^{3x})

\frac{\partial}{\partial x} (e^{3 x})

limit as x approaches-9+of (6x+54)/(x+9)

x \to - 9 + lim (\frac{6 x + 54}{x + 9})

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9 x^{4} - 9 x^{2}, 10 x^{2}

derivative of (1/(x^2-7/(x^4))(x+3x^3))

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{7}{x ^{4}}) (x + 3 x^{3}))

Frequently Asked Questions (FAQ)

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