00:02
So here we are asked to differentiate between the simple and the general power rule.
00:14
And to illustrate that, first we'll let y be equal to ax to the n, where a is a constant.
00:27
To find a derivative with respect to x, what we do is that we bring down the n first, and then we multiply it by the entire function, but you will be a derivative.
00:55
Is a x and in the power we subtract one.
01:01
Then we go ahead to multiply by the derivative of just the x.
01:14
Now notice that the derivative of x is just one and one times any number still remains the same so it can be ignored always for these type of functions.
01:35
So this means the derivative would be n times a x.
01:40
X to the n minus 1.
01:45
Whenever this happens, we call it the simple power rule.
01:53
So an example would be y equals 2x to the 4.
02:02
So to do this, we bring down the 4, and we multiply it by the function 2x, and in the power, we subtract 1.
02:19
So that gives us 8x to the 3rd.
02:27
Now we'll consider another kind of function, which is a times a certain function of x to the n.
02:40
And the difference between this and the first one is that this is just the constant times the x to a certain power.
02:48
But in this case, you would have a certain kind of functions such as, let's say, 2x minus 1 or x and then something else.
02:57
What i mean to say is that the x is not by itself...