00:01
Alright, so we have some function y in terms of t and we want to find the derivative.
00:05
I like to write it as a product because the product rule is way easier than the quotient rule.
00:11
Also, t minus 2 in the square root can be written as t minus 2 to the 1 half power.
00:19
It's easier to work with powers.
00:21
So then this the denominator t cubed plus 2 we raised to the negative 1 like so.
00:31
Alright, so keep one term the same so we could keep the t minus 2 to the 1 half and then we take the derivative of the other term.
00:40
So bring the power down and then t cubed plus 2 decrease the power from negative 1 to negative 2.
00:48
Chain rule take the derivative of the inside which is going to be 3t squared.
00:53
Now for the second term we're taking the derivative of this now which we kept constant.
00:58
So bring the power down t minus 2 1 half minus 1 is negative 1 half.
01:09
The derivative of t is just 1 and then we have the t cubed plus 2 to the negative 1.
01:17
Now let's go ahead and simplify...