Derivative of f(x)=(square root x^2-2x)^3-9(square rootx^2-2x)

use the prower rule and the chain rule. they are in your book or online.

 

[tex]f(x) = (\sqrt{x^2 - 2x})^3 - 9\sqrt{x^2 - 2x}[/tex]

Just like what Mathwonk said, use the chain rule for the first one
[tex] (\sqrt{x^2 - 2x})^3[/tex]

[tex] \sqrt{x^2 -2x} [/tex] is the inside function g(x) and [tex] x^3 [/tex] is the outer function f(x)

The chain rule states, [tex] h '(x) = f '(g(x)) * g'(x) [/tex]



For the power rule, for
[tex]f(x)g(x) [/tex], the derivative is [tex]f'(x)g(x) + g'(x)f(x)[/tex]

I'm giving you this information because you can find it in your book. Its up to you to find those inside and outer functions and differentiating them

 

That's the product rule. Power rule:

[tex]\frac{d}{dx} x^n = nx^{n - 1}[/tex]

 

Of course, to use the power rule you will need to know that [tex]\sqrt{x}= x^{\frac{1}{2}}[/tex].