Derivative Rules?

[EvoN1020v]

I am having a problem here. I can't figure this out.

 

[math]y=(3x-2)^4[/math] is [math]81x^4 - 216x^3 + 198x^2 - 96x + 16[/math].

 

The derivative for the above function is [math]y\prime = 12(3x-2)^3[/math].

 

The question is asking me to find out the pattern and write it is as an equation in the same form of the power rule. ([math]y=ax^n[/math] is [math]y\prime = anx^{n-1}[/math]).

 

This goes same for [math]y=(2x^2 + 3)^5[/math] which is [math]y\prime = 20x(2x^2 + 3)^4[/math].

 

I got [math]y=(ax+p)^n[/math] and [math]y\prime = an(ax+p)^{n-1}[/math], which worked for the first function, but not the second. My teacher said that for the second function, "You know that 2 x 2 x 5 is 20. How can you make [math](2x^2)(5)[/math] be 20x. You will need to take 2 derivatives."

 

Do you guys know any equation that will fit both functions?

[Dave]

Here's a hint. If you have a function of the form [math]f(x) = (x^n+1)^m[/math], let [math]u(x) = x^n + 1[/math]. Then we get a function [math]f(u) = u^m[/math]. Construct an equation for [math]\frac{df}{dx}[/math] by considering [math]\frac{df}{du}[/math] and [math]\frac{du}{dx}[/math].

[ydoaPs]

in other words, use the chain rule.

[Dave]

Given the type of assignment he's giving, I'm betting this is a precursor to the chain rule - which is why I explicity didn't say so

[ydoaPs]

I noticed your sig. Why not post it on IDF?