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Popular >

derivative of 2/(1-x)

Solution

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

Solution

\frac{2}{( 1 - x ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= 2 (- \frac{1}{( 1 - x ) ^{2}} (- 1))

Simplify

2 (- \frac{1}{( 1 - x ) ^{2}} (- 1)) : \frac{2}{( 1 - x ) ^{2}}

= \frac{2}{( 1 - x ) ^{2}}

Popular Examples

limit as x approaches-5-of (-4x)/(x+5)

x \to - 5 - lim (\frac{- 4 x}{x + 5})

integral of (ln(t)t^{-1})/(-3)

\int \frac{ln ( t ) t ^{- 1}}{- 3} d t

derivative of ln(x^2+y^3)

\frac{d}{d x} (ln (x^{2} + y^{3}))

integral of x^3sqrt(4-x^2)

\int x^{3} 4 - x^{2} d x

integral of (5x^3-3x^2+2)/(2x^2)

\int \frac{5 x ^{3} - 3 x ^{2} + 2}{2 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of 2/(1-x) ?
The derivative of 2/(1-x) is 2/((1-x)^2)
What is the first derivative of 2/(1-x) ?
The first derivative of 2/(1-x) is 2/((1-x)^2)