differentiate the following trigonometric functions

Question

1.   cos2x      3.   sin²x       3.    sin(2x-3)          4.         sinxcosx

Answer 1

Moses,

(1) d(cos2x)/dx = -sin(2x)d(2x)/dx = -2sin(2x)

 

(2) d(sin²x)/dx = 2sinx(dsinx/dx) = 2sinx(cosx) 

 

(3) d(sin(2x-3))/dx = cos(2x-3)d((2x-3)/dx) = 2cos(2x-3)

 

(4) d(sinxcosx)/dx = cosx d(sinx)/dx + sinx d(cosx)/dx = cos²x - sin²x