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^n1 * 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^24x+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 = 6x4, so the final answer is
df/dx = 5(3x^24x+5)^4 (6x4)
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