What is the 87th derivative of sin x?

Answer 1

Every fourth derivative, you get back to "sin x" - in other words, the 84th derivative of "sin x" is also "sin x". From there, you need to take the derivative 3 more times, getting:85th derivative: cos x86th derivative: -sin x87th derivative: -cos x

Answer 2

The 1st derivative of the sin is cos; the 2nd is -sin; 3rd is -cos; 4th is sin; then repeats every fourth time. So 84 th is the sin; 85th cos; 86th -sin; and 87th derivative is -cos