00:01
In this question, we are asked to find the 19th derivative of sine x.
00:04
Well, let's try to do the first few derivatives.
00:07
Y ' equals cos x.
00:10
So, this is the first derivative.
00:12
Y' ' equals negative sine x, which is the second derivative.
00:20
The third derivative is negative cos x.
00:25
The fourth derivative, and we'll write it like this, equals sine x, because the derivative of cos is negative sine, and two negative sines give you a positive sine.
00:36
The fifth derivative equals cos x.
00:42
The sixth derivative is negative sine x.
00:49
The seventh derivative is negative cos x.
00:56
The eighth derivative is sine x.
01:02
Now look at the pattern.
01:05
The first derivative is cosine.
01:08
The fifth derivative is cosine.
01:11
And the ninth derivative would also be a cosine.
01:15
The second derivative is negative sine.
01:18
The sixth derivative is negative sine.
01:22
The third derivative is negative cosine.
01:24
The seventh derivative is negative cosine.
01:26
The fourth derivative is sine...