00:01
So in this question, i want to use the power rule to find the derivatives of each of the following functions.
00:06
In a, i want the derivative of f of x equals x to the negative third power.
00:14
So to find my derivative, f prime of x, what do i do? i multiply the exponent down, negative three, x take one away from the exponent to the negative fourth power.
00:28
So that i have negative three over x of the fourth power.
00:33
And there's my answer to a.
00:36
In b, i want my derivative of f of x equals 4 over x squared minus 10x cubed.
00:44
I'm going to start by rewriting my original function.
00:47
My function f of x could be rewritten as 4x to the negative second, if i flip that up, minus 10x cubed, which means that my derivative, using the power rule, multiply the negative 2 down, negative 8x to the negative third power, minus 3rd power, minus 3rd.
01:11
Times x squared.
01:14
Now, i clean this up to get rid of my negative exponent, negative 8 over x cubed, minus 30 square.
01:27
In c, i want my derivative of f of x equals 2 plus the squared of x.
01:37
Remember that the squared of x is x to the one -half power.
01:42
So i start by rewriting square root of x as x to the one -half.
01:48
Let's get our derivative...