Question

f(x)=x^2/sqrt(x^2-a^2) , find f'(x)

Answer 1

use quotient rule
\[f'(x)=\frac{(x^2)'\sqrt{x^2-a^2}-x^2 (\sqrt{x^2-a^2})'}{(\sqrt{x^2-a^2})^2}\]

Answer 2

\[f'(x)=\frac{2x \sqrt{x^2-a^2}-x^2 \frac{1}{2}(x^2-a^2)^{\frac{1}{2}-1}(x^2-a^2)'}{x^2-a^2}\]

Answer 3

Thanks !