00:02
Hello, in this question we are given some functions of x and we have to find f ' of x.
00:08
Okay, so f ' of for the first function is minus 2 cos x plus 7 sin x then this implies f ' of x is minus 2, derivative of cos x is minus sin x plus 7, derivative of sin x is cos x which is equal to 2 sin x plus 7 cos x.
00:54
Okay, now here plus 5 sec x this implies f ' of x is equal to, we are going to use product, we are going to use, let me write it in the next line, we don't have enough space to write the product line, sorry to write the product rule.
01:33
So if fx equal to this thing f ' of x is equal to, we are going to use product rule so it is 2x sin x plus x square, derivative of sin x is cos x and derivative of sec x is sec x tan x.
01:57
So it is 5 sec x tan x and to finally we have fx equal to sin x over 1 minus cos x.
02:16
We are going to use, we are going to use quotient rule.
02:20
So f ' of x is 1 minus cos x times derivative of sin x which is cos x minus sin x, derivative of 1 minus cos x is minus minus sin x which is plus sin x.
02:54
So divided by 1 minus cos x square, 1 minus cos x square, this thing is cos x minus cos square x minus sin square x divided by 1 minus cos x whole square...