00:01
In this problem, we are asked to find the derivative of the function, y equals 5 x -rays to the negative 5 minus 6 x -rays to the negative 2 plus 13 x -rays to the negative 1.
00:16
We know that the derivative of the sum or difference of functions is same as the sum or difference of their derivatives.
00:26
So here we have three functions, 5 x -rays to the next.
00:31
Negative 5, 6 x raised to the negative 2, and 3 x raised to the negative 1.
00:36
So the derivative, dy over d x, is going to be d over d x of 5 x raised to the negative 5, minus d over d x of 6 x raised to the negative 2, plus d over d x of 13 x raised to the negative 2, 1.
01:04
Notice that in each of the individual derivatives, 5, 6, and 13 are the constants, so which we can just pull out because the derivative of a constant times a function is same as constant times the derivative of the function.
01:22
So it becomes 5 times d d d x of x raised to the negative 5 minus 6 times d d x of x raise to the negative 2 plus 13 times d d x of x raised to the negative 1...