What is the derivative of sqrt(4/(x^2-1)) ?

The derivative of sqrt(4/(x^2-1)) is -(2x)/((x^2-1)^{3/2)}

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

The first derivative of sqrt(4/(x^2-1)) is -(2x)/((x^2-1)^{3/2)}

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

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

Solution steps

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

Apply the chain rule:

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

= \frac{1}{2 \frac{4}{x ^{2} - 1}} \frac{d}{d x} (\frac{4}{x ^{2} - 1})

\frac{d}{d x} (\frac{4}{x ^{2} - 1}) = - \frac{8 x}{( x ^{2} - 1 ) ^{2}}

= \frac{1}{2 \frac{4}{x ^{2} - 1}} (- \frac{8 x}{( x ^{2} - 1 ) ^{2}})

Simplify

\frac{1}{2 \frac{4}{x ^{2} - 1}} (- \frac{8 x}{( x ^{2} - 1 ) ^{2}}) : - \frac{2 x}{( x ^{2} - 1 ) ^{\frac{3}{2}}}

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

y = x^{2} + 2 x + 6

x^{2}, x + 2, 0

x \to 0 lim (\frac{e ^{x} - 1}{3 x})

f (x) = (4 x - 7)^{\frac{1}{2}}, at x = 4

\int e^{x} x^{2} d x

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