Find the derivative of the function f(x)=(2x+1)(3x=4)2?

Answer 1

i assume thats f(x) = (2x+1)(3x+4)*2
If so:
Method one:
multiply out the brackets to get 12x^2 + 22x + 8
Then use the rules for differentiation d/dx(x^2) = 2x, d/dx(x) = 1, d/dx(constant) = 0 and d/dx(C*g(x)) = C*d/dx(g(x)) to get
d/dx(f(x)) = 24x+22

Method two:
Use the chain rule
(uv)' = u'v + v'u where ' denotes d/dx

so f'(x) = 2*(2(3x+4) + 3(2x+1)) = 2(6x + 8 +6x +3) = 24x + 22

which agrees with the above answer.

Answer 2

there are a hundred different ways to solve this. i'm going to assume that you meant (3x-4) for this. but you can either use the limit definition of a derivative, the product rule, or you can combine all those terms and use the power rule. me personally, i'd use the power rule just because i'm more comfortable with that at this point. if you want to find out more on this stuff, just do a search. i won't show you the whole solution, but the answer is f'(x)=24x-10

Answer 3

I'm assuming you meant:
f(x)=(2x+1)(3x+4)2
2(6x^2+8x+3x+4) = 12X^2+22x+8
f'(x) = 24x+22

Answer 4

what is x