# Math Help - Finding derivatives using the product rule

1. ## Finding derivatives using the product rule

I'm having trouble getting the correct answer when using the product rule to find a derivative.

For example when using the product rule to solve ((3x+1)^(3/2))*(2x+4)
I end up with the answer 9x^(3/2)+18x^(1/2)+6x^(3/2)+2^(3/2)

however my textbook says the answer is (5(3x+1)^(1/2))*(3x+4)

how do I get the answer in this form???

2. ## Re: Finding derivatives using the product rule

Originally Posted by JellyOnion
I'm having trouble getting the correct answer when using the product rule to find a derivative.

For example when using the product rule to solve ((3x+1)^(3/2))*(2x+4)
I end up with the answer 9x^(3/2)+18x^(1/2)+6x^(3/2)+2^(3/2)

however my textbook says the answer is (5(3x+1)^(1/2))*(3x+4)

how do I get the answer in this form???

Let's see:

you would actually use product rule with chain rule(for this (3x+1)^(3/2)), so we will have -

f'(x) = ((3x+1)^(3/2))' * (2x+4) + ((3x+1)^(3/2))*(2x+4)' =

(3/2)*(3x+1)^(1/2) *(3)*(2x+4) + ((3x+1)^(3/2))*(2x) =

3(3x+1)^(1/2) *(2x+4) + ((3x+1)^(3/2))*(2x) =...

would you need any help further to factorize or you are ok?

3. ## Re: Finding derivatives using the product rule

Originally Posted by JellyOnion
I'm having trouble getting the correct answer when using the product rule to find a derivative.

For example when using the product rule to solve ((3x+1)^(3/2))*(2x+4)
]
So this is of the form f(x)g(x) with f(x)= (3x+ 1)^(3/2) and g(x)= 2x+ 4.
Of course, the product rule says (fg)'= f'g+ fg'
With f(x)= (3x+ 1)^{3/2}, f'(x)= (3/2)(3x+1)^(1/2)(3)= (9/2)(3x+1)^{1/2} and with g(x)= 2x+ 4, g'(x)= 2.
f'g= (9/2)(3x+1)^{1/2}(2x+ 4) and fg'= 2(3x+1)^{3/2}
[quote]I end up with the answer 9x^(3/2)+18x^(1/2)+6x^(3/2)+2^(3/2)[quote]
You appear to be thinking that (9/2)(3x+ 1)^(1/2)(2x+ 4)= (9/2)[3x^{1/2}+ 4](2x+4) and that 2(3x+1)^{3/2}= 2(3x^{1/2}+ 1).
That is NOT true. In particular, (3x+1)^{3/2} is NOT 3x^(3/2)+ 1.

however my textbook says the answer is (5(3x+1)^(1/2))*(3x+4)

how do I get the answer in this form???