Derivative:

Question

Derivative:

anonymous · Answer

sure of what function?

luigi0210 · Answer

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

ivancsc1996 · Answer

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

ivancsc1996 · Answer

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

zepdrix · Answer

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 :)

luigi0210 · Answer

Couldn't you also use implicit differentiation?

primeralph · Answer

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