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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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