Question

Find the 96 th derivative of f(1) = sin c.
f (96) (2)
=

Answer 1

The derivatives of sin(x) follow a simple pattern:

f(x) = sin(x)

f '(x) = cos(x)

f ''(x) = - sin(x)

f '''(x) = - cos(x)

f ''''(x) = sin(x)

and so on. 96 is a multiple of 4, so

f ⁽⁹⁶⁾(x) = sin(x)