find the derivative of f(x)=(2x+1)^3(3x-2)^2 and simplify to a single term.

4(2x+1)^3 (3x-2) + 9(2x+1)^2 (3x-2)^2 I have this so fare.

Question

find the derivative of f(x)=(2x+1)^3(3x-2)^2 and simplify to a single term.

4(2x+1)^3 (3x-2) + 9(2x+1)^2 (3x-2)^2  I have this so fare.

anonymous · Answer

combine the like terms ( 2x+1) and (3x-2)
ans simplify

anonymous · Answer

if you multiply it all out you will get a function involving powers of x and a constant.
But notice that this is a function of of ( 2x+1) and (3x-2), you can probably factor the binomial and make this a bit easier.

anonymous · Answer

say you want to simplify: 4(2x+1)^3 (3x-2)
By the binomial theorem, (2x+1)^3=8x^3+12x^2+6x+1
(8x^3+12x^2+6x+1)(3x-2)=24x^5+20x^3-6x^2-9x-2
that's the model for the first, now do the second one. it takes a long time, but you just have to be patient and meticulous. :)

zarkon · Answer

Factor out $$(2x+1)^2$$ and $$3x-2$$

you will end up with $$6(2x+1)^2(3x-2)(5x-1)$$

anonymous · Answer

easier method use u and v 
u=2x+1
v=3(3x-2)^2

anonymous · Answer

so then its simply u^v

anonymous · Answer

In the formula you posted you have the coefficients wrong.  It looks like you got confused about what derivative to multiply by when doing the chain rule.  You should get 6 for both coefficients.  Zarkon's answer is correct.