Posted: **Feb 17, 2012 10:09 am**

by **Darkchilde**

EXAMPLES FOR CONSTANTS AND POWERS

For the following functions, please find the first and second derivatives:

- [math]f(x)=x^3+2
- [math]f(x)=5x^7+x^{-5}
- [math]f(x)=8x^{-3}-9x^7-4
- [math]f(x)=bx^f+c

where b,f and c are constants

Let's start solving:

- We are given the equation [math]f(x)=x^3+2. Remember that the derivative of this is the addition of each term, as each term can be seen as a separate function. So, we start with the first term: [math]x^3. What is its derivative? Remembering the rule, a=1, n=3 and n-1=2. Then the derivative of this is: [math]3x^2. The second term is 2, which is a constant and so its derivative is equal to 0. Adding those two we get the following:

[math]f'(x)=3x^2

There is no need to add the 0, the derivative of the 2 term.

We also need the second derivative; just follow the same rule and we have: a=3, n=2 and n-1=1. So, the second derivative is:

[math]f''(x)=3\times 2\times x

[math]f''(x)=6x

Think the other three for today. Post your solutions in spoilers in the discussion thread, and I will give the full solution tomorrow.