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Popular >

derivative of ((1+x/(1-x))^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 \cdot \frac{1 + x}{1 - x} \cdot \frac{2}{( 1 - x ) ^{2}} : \frac{4 ( 1 + x )}{( 1 - x ) ^{3}}

= \frac{4 ( 1 + x )}{( 1 - x ) ^{3}}

Popular Examples

(d^4)/(dx^4)(1/(3x+1))

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

integral of 2x^3+4x+5

\int 2 x^{3} + 4 x + 5 d x

limit as x approaches pi of sin(11/6)

x \to π lim (sin (\frac{11}{6}))

derivative of 1/8 x^4-(32)/(x^3)derivative of

\frac{1}{8} x^{4} - \frac{32}{x ^{3}}

integral from-4pi to 4pi of (sin^2(x)+1)

\int_{- 4 π}^{4 π} (sin^{2} (x) + 1) d x

Frequently Asked Questions (FAQ)

What is the derivative of ((1+x/(1-x))^2) ?
The derivative of ((1+x/(1-x))^2) is (4(1+x))/((1-x)^3)
What is the first derivative of ((1+x/(1-x))^2) ?
The first derivative of ((1+x/(1-x))^2) is (4(1+x))/((1-x)^3)