What is the derivative of (1+sqrt(x)/(1-sqrt(x))) ?

The derivative of (1+sqrt(x)/(1-sqrt(x))) is 1/(sqrt(x)(1-\sqrt{x))^2}

What is the first derivative of (1+sqrt(x)/(1-sqrt(x))) ?

The first derivative of (1+sqrt(x)/(1-sqrt(x))) is 1/(sqrt(x)(1-\sqrt{x))^2}

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

f (x) = x ∣ x ∣

f (x) = 5 x - 4

\int_{\frac{1}{3}}^{5} 12 x ln (3 x) d x

\int tan^{2} (x co) s^{3} x d x

x \to - 2 lim (\frac{- 3}{x + 2})

What is the derivative of (1+sqrt(x)/(1-sqrt(x))) ?
The derivative of (1+sqrt(x)/(1-sqrt(x))) is 1/(sqrt(x)(1-\sqrt{x))^2}
What is the first derivative of (1+sqrt(x)/(1-sqrt(x))) ?
The first derivative of (1+sqrt(x)/(1-sqrt(x))) is 1/(sqrt(x)(1-\sqrt{x))^2}