please do the following problems and show the work

74. Use the definition of the derivative to find the derivative of cos(r). Use your result to complete Theorem 34 Theorem 34 (Derivative of the Cosine) dr COBI = 75. Calculate the following derivatives: (a) I sin (2x) = (b) - sin(x) cos(e]) = (c) - esin r = dr d (d) de - In | cos #| = 76. Recall that tan T = 281' minx. Use the quotient rule to find tan r. Simplify completely. dr Use your result to fill in the conclusion for Theorem 35