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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{'}} + 4 y = e^{- 4 t}

\frac{d}{d x} (\frac{7 x}{x ^{2} + 1})

\int \frac{1}{x ^{2} + 5} d x

sin (y) d x + cos (x) d y = 0

x, - 3, 16, 1

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