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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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