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

[candynrg]

How do I find the derivative of f(x)=(square root x^2-2x)^3-9(square rootx^2-2x)

 

[mathwonk]

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

 

[PhysicsinCalifornia]

How do I find the derivative of f(x)=(square root x^2-2x)^3-9(square rootx^2-2x)

f(x) = (\sqrt{x^2 - 2x})^3 - 9\sqrt{x^2 - 2x}

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

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

The chain rule states, h '(x) = f '(g(x)) * g'(x)



For the power rule, for
f(x)g(x), the derivative is f'(x)g(x) + g'(x)f(x)

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

 

[Nylex]

For the power rule, for
f(x)g(x), the derivative is f'(x)g(x) + g'(x)f(x)

That's the product rule. Power rule:

\frac{d}{dx} x^n = nx^{n - 1}

 

[HallsofIvy]

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