Question

Derivative:

Answer 1

sure of what function?

Answer 2

\[f(x)=\sqrt{\frac{(x+5)(x-3)}{(x+2)(x-1)}}\]

Answer 3

\[f'(x)=\frac{ 1 }{ 2\sqrt{\frac{ (x+5)(x-3) }{ (x+2)(x-1) }} }\frac{ (2x-3+5)(x+2)(x-1)-(x+5)(x-3)(2x-1+2) }{ (x-2)^{2}(x-1)^{2} }\]

Answer 4

Wow im sorry, it sould read an (x+2)^2 in te denominator, not an (x-2)^2

Answer 5

The derivative of \(\large \sqrt{x}\) gives us \(\large \dfrac{1}{2\sqrt{x}}\)

From there you apply the chain rule, multiply by the derivative of the inside.\[\large \dfrac{1}{2\sqrt x}x'\]

So as you see what ivan did, he worked out the quotient rule.
And then you have the product rule within the quotient rule.

It's a bit of a tricky problem :)

Answer 6

Couldn't you also use implicit differentiation?