Posted by **cathy** on Wednesday, July 18, 2012 at 12:43pm.

I need to find the derivative and can't do them when they are raised to powers? Thank You.

m(x)x^5 - 5x^3+7x -4)^10 (4x^9 +19)^23 this on is tuff!

- calculus/derivatives -
**Reiny**, Wednesday, July 18, 2012 at 12:56pm
Your brackets don't match , also there is no equal sign

is it ...

m(x) = (x^5 - 5x^3 + 7x - 4)^10 * (4x^9 + 19)^23 ??

(the * means multiplication)

- calculus/derivatives -
**Steve**, Wednesday, July 18, 2012 at 2:09pm
the key, however, is the chain rule. If

f = u^n, then

df/dx = nu^n-1 * du/dx

It's just the familiar power rule, but you have to multiply by the derivative of what's raised to the power.

For example, if you have

f(x) = (3x^2-4x+5)^5, then

let u = 3x^2 - 4x + 5.

Then all you have is

f(x) = u^5

df/dx = 5u^4 du/dx

But that's easy, because du/dx = 6x-4, so the final answer is

df/dx = 5(3x^2-4x+5)^4 (6x-4)

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