00:01
So to find this derivative function, we're going to go ahead and set it up, and then we're going to cut it up into four different derivatives.
00:08
So if we're looking at the derivative as a whole, it's going to be equal to the derivative of x to the fourth divided by four minus x cubed divided by three, plus x squared divided by two, and then plus x divided by one, which is just x.
00:24
So we're looking at this derivative as a whole.
00:26
And oh sorry actually this um this last term should have been minused so minus x and so since we just have a bunch of terms being added or subtracted together what we can do is we can cut this up into four different derivatives and so this is equal to the derivative x to the fourth divided by four minus the derivative of x cubed divided by three plus the derivative of x squared divided by 2 and then minus the derivative of x.
00:58
And what we can do now is we can bring out each of these constants.
01:01
So here we have a constant of one -fourth, here one -third and one -half.
01:06
So this is going to be one -fourth times the derivative of x to the fourth, and then minus one -third times the derivative of x to the third, and then plus a half times the derivative of x squared, and this one is still just the derivative of x.
01:23
So now to find each of these derivatives, i'm just going to use the power rule, which i'll go ahead and write down here, where we have the derivative of x raises some power n.
01:31
That's equal to n times x to the n minus one power...