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### 2nd Derivative

```
Date: Mon, 21 Nov 94 10:49:33 AST
From: "Jim Mullen"
Subject: math problem

I am a grade twelve student taking calculus and was wondering if you could
help me with this problem.
y=2x(6x+5)exp4
solve to the second derivative
Any help will be greatly appreciated!
```

```
Date: Mon, 21 Nov 1994 10:47:55 -0500 (EST)
From: Dr. Ken
Subject: Re: math problem

Hello there!

I think the way that we would write your function is 2x(6x+5)^4.  Is that
right?  It looks like we're going to have to use the product rule a couple
of times to take two derivatives of your function.  Have you seen the
product rule before?  Here it is:  [f(x)g(x)]' = f'(x)g(x) + f(x)g'(x).

So here's how it applies in our situation:  we take the derivative of 2x,
mulitiply that by (6x+5)^4, and then add that to 2x times the derivative of
(6x+5)^4.

So we get 2(6x+5)^4 + 48x(6x+5)^3 as our first derivative.  Do you see why?
The next step, finding the second derivative, will be very similar, and I'll
let you try it yourself.  Write back if you have more questions!

-Ken "Dr." Math
```
Associated Topics:
High School Calculus

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