Derivatives of Trigonometric Functions

Question

f (x) = 5sinx / (1+cosx)

f '(x) =

Answer 1

Solution:

f (x) = 5sinx / (1+cosx), This function is of the form u/v and the derivative of it is u'v - v'u / v²

Let u = 5sinx, u' = 5cosx , and v = 1+cosx, v' = -sinx

f'(x) = u'v - v'u / v² = 5cosx(1+cosx) - (-sinx)(5sinx) / ( 1+cosx)²

= 5cosx + 5 cos²x + 5 sin²x / ( 1+cosx)² = 5 cosx + 5( cos²x + sin²x) / (1+cosx)²

= 5cosx + 5(1) / ( 1+cosx)² = 5( 1+cosx) / ( 1+cos)(1+cosx) = 5 / (1+cosx)