Question

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

Answer 1

\[\frac{\delta}{\delta x}[\frac{x^2}{\sqrt{x^2-a^2}}]=\frac{x^3-a^2x}{(x^2-a^2)^{3/2}}\]

Answer 2

Can you show steps?

Answer 3

Product Rule:
\[=x^2(\frac{d}{dx}(\frac{1}{\sqrt{x^2-a^2}})+\frac{2x}{\sqrt{x^2-a^2}}\]
Chain Rule:
\[\large =x^2-\frac{\frac{d}{dx}(x^2-a^2)}{2(x^2-a^2)^{3/2}}+\frac{2x}{\sqrt{x^2-a^2}}\]
\[\large=\frac{2x}{\sqrt{x^2-a^2}}-\frac{x^2(2x)}{2(x^2-a^2)^{3/2}}\]
do the subtraction and you get what i first put.

Answer 4

Thanks!