Question

Find the given derivative by finding the first few derivatives and observing the pattern that occurs? `((d^107)/(dx^107))*(sin(x))`

Answer 1

`-cos x`

Explanation:

`d/dx sin x = cos x`
`d^2/dx^2 sin x= - sin x`
`d^3/dx^3 sin x= - cos x`
`d^4/dx^4 sin x= sin x`

So, every fourth derivative of `sin x` is back to `sin x`. Thus the 104th derivative of `sin x` is also `sin x`, and the 107th derivative is the same as the third.