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

The derivative of f(x)=sqrt((1+x)/(1-x)) is 1/(sqrt(x+1)(-x+1)^{3/2)}

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

The first derivative of f(x)=sqrt((1+x)/(1-x)) is 1/(sqrt(x+1)(-x+1)^{3/2)}

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derivative of

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

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

Solution steps

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

Apply the chain rule:

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

= \frac{1}{2 \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}}

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

Simplify

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

= \frac{1}{x + 1 ( - x + 1 ) ^{\frac{3}{2}}}

x \to 1 lim (e^{4 x^{2} - 4 x})

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

f (x) = 3 arccos (\frac{x}{2})

\frac{d}{d x} (\frac{3 x}{5 x ^{2} - 2 x - 9})

y = x^{2} - 18, y = 17 x

What is the derivative of f(x)=sqrt((1+x)/(1-x)) ?
The derivative of f(x)=sqrt((1+x)/(1-x)) is 1/(sqrt(x+1)(-x+1)^{3/2)}
What is the first derivative of f(x)=sqrt((1+x)/(1-x)) ?
The first derivative of f(x)=sqrt((1+x)/(1-x)) is 1/(sqrt(x+1)(-x+1)^{3/2)}