find d/dx (sin^(21)x *cos21x)

Answer 1

If that's sin(21x)*cos(21x) then

f = 1/2 sin(42x)
f' = 21cos(42x)

or, directly,

f' = 21cos(21x)cos(21x) - 21sin(21x)sin(21x)
= 21cos²21x - 21sin²21x

On the other hand, if that's

f = sin²¹x*cos²¹x, then we have

f' = 21sin²⁰x cos²²x - 21sin²²x cos²⁰x
= 21sin²⁰x cos²⁰x (cos²x - sin²x)
= 21sin²⁰x cos²⁰x cos2x