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???

thanks to everyone in advance (Happy)

Re: Finding derivatives using the product rule

Quote:

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???

thanks to everyone in advance (Happy)

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?

Re: Finding derivatives using the product rule

Quote:

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.

Quote:

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

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

thanks to everyone in advance (Happy)

Re: Finding derivatives using the product rule

Thank you dokrbb very much for your help but I'm still a little confused how you would factorize that to the answer.

Re: Finding derivatives using the product rule

Ohhh thanks hallsoivy i see, very much appreciate the help