Posted: Feb 19, 2012 8:38 am
This post will be about solving the third example:
Again we use the exact same methodology to differentiate the above example. Let's see it all term by term, and start differentiating:
So, for the first term we have: a=8, n=-3 and n-1=-3-1=-4; then the derivative for this term is:
Proceeding to the second term:
Here we have: a=-9, n=7 and n-1=7-1=6. Then this derivative will be:
The third term is a constant, -4, and so its derivative is equal to 0. So, the first derivative of our function will be equal to:
We also want to find the second derivative; again we follow the same method, as before.
We have a=-24, n=-4 and n-1=-4-1=-5; so the second derivative of the above will be:
And continuing with the second term of the first derivative:
Here we have a=-63, n=6 and n-1=6-1=5. Plugging in the numbers we get:
Putting the two terms together, we get the second derivative of our function:
Always remember to check the signs of each function; as I said earlier, a change of sign will give a vastly different result. I will do the last example later this afternoon.
[math]
Again we use the exact same methodology to differentiate the above example. Let's see it all term by term, and start differentiating:
[math]
So, for the first term we have: a=8, n=-3 and n-1=-3-1=-4; then the derivative for this term is:
[math]
[math]
Proceeding to the second term:
[math]
Here we have: a=-9, n=7 and n-1=7-1=6. Then this derivative will be:
[math]
[math]
The third term is a constant, -4, and so its derivative is equal to 0. So, the first derivative of our function will be equal to:
[math]
We also want to find the second derivative; again we follow the same method, as before.
[math]
We have a=-24, n=-4 and n-1=-4-1=-5; so the second derivative of the above will be:
[math]
[math]
And continuing with the second term of the first derivative:
[math]
Here we have a=-63, n=6 and n-1=6-1=5. Plugging in the numbers we get:
[math]
[math]
Putting the two terms together, we get the second derivative of our function:
[math]
Always remember to check the signs of each function; as I said earlier, a change of sign will give a vastly different result. I will do the last example later this afternoon.