Posted by **becky** on Friday, August 25, 2006 at 10:29pm.

I've been having some difficulities with this but I think I figured it out. Could you double check me and make sure I'm doing the correct steps?

Differentiate and simplify the answer.

f(x) = 2(3x+1)^4 (5x-3)^2

=2(3x+1)^4 [2(5x-3)(5)] + [8(3x+1)^3] (5x-3)^2

=2(3x+1)^4 [10(5x-3)] + [24(3x+1)^3] (5x-3)^2

=2(3x+1)^4(5x-3)[34(3x+1)^3(5x-3)]

I hope I'm getting this now.

On the very first step, you forgot to use the chain rule in the second half of the sentence.

Looks like you have the concept of deriving the product of two equations correct.

Becky, here's a suggestion for doing the chain rule. Construct a table like this: Let g = (3x+1) and h = (5x-3).

Then g' = 3 and h' = 5.

What we have then is:

f = 2(g^4)(h^2)

Now differentiate the symbols first, then substitute for them.(We treat f,g,h as functions of x.)

So, f' = 2[(4g^3g')h^2 + g^4(2hh')]

Now factor out 2(g^3)h to get,

f' = 2*2*(g^3)h[2g'h + gh']

Now substitute for the symbols above. Further simplifying might be possible too.

If you use this approach you should make fewer errors I think. In first yr calc you'll probably see longer expressions than this one, some with 3 or even 4 functions and composite functions. Creating a table of symbols and doing the calc on them will save a lot of writing and potential errors.

## Answer This Question

## Related Questions

- calculus - I have been asked to solve this two different ways. The first way is ...
- Calculus - I'm having problems with this one. Can't get the right answer. ...
- Math (Calculus) - Hello, Could somebody please help me with the following ...
- MoRe HeLp PlEaSe!! (calc) - Also can I get some help with this LONG, TIRESOME ...
- Calculus - Differentiate using the chain rule: y=(x+(x+x^(1/2))^(1/2))^(1/2) y...
- Math-The chain rule HELP - Use the chain rule and simplify your answer: y= 1/u ...
- math-check - I have solved the following questions, let me know if they are ...
- chem-repost - I ddin't know if anybody would look far down to page to help me ...
- maths - differentiate using product, chain and quotient rule ln x / 5x-7 and e^x...
- Calculus - How do I use the chain rule to find the derivative of square root(1-x...

More Related Questions