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

Simplify

\frac{1}{2 \frac{x ^{2} - 1}{x ^{2} + 1}} \cdot \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}}}

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)}