Calculus Question. Please Help

Question

Evaluate the derivative of the following function.

Find [(d^99)/(dx^99)](sinx)

Answer 1

Hi Kayla, this question involves the "trick" of trig derivatives. The first four are distinct, then it repeats. Take f(x) = sinx. The first derivative is cosx, the second derivative is -sinx, the third derivative is -cosx, the fourth derivative is back to sinx. To find the n^th derivative, divide n by four and look at the remainder.

For example, if we wanted the 65th derivative of sin(x), we could do 65 / 4 = 16.25 or 16 and 1/4. 1 is the remainder, so the 65th derivative is the same as the 1st derivative of sin(x), which is cos(x). Repeat this process for the 99th derivative