00:01
Okay, so before we complete these examples, let's review power rule.
00:04
What is power rule? it's just a simplified way to find the derivative of a function.
00:08
So given y x to the nth exponent, my derivative y subprime, for power roll, i just bring down my exponent in front of my x term and then subtract one from my exponent.
00:20
So for example, to find the derivative of y, x the third, this would just be bring down the three over two times x to the three over two.
00:30
2 minus 1.
00:32
Okay, what's 3 over 2 minus 1? this is the same as 3 over 2 minus 2 over 2.
00:38
So this will be 3 over 2 times x x to the 1 half.
00:43
What's anything to the rational exponent? well, this is just going to be this 3 over 2 times squared x.
00:49
Okay, so this is my derivative.
00:51
What does my derivative mean? well, my derivative is actually representing all the different forms of the slope of each of the point.
00:58
So let's say i wanted to find the slope at the point 1 -1.
01:01
I can plug in my x value into the derivative.
01:04
So i could say 3 over 2 times the square root of 1...