Umm Al-Qura University بسم الله الرحمن الرحيم Umm Al-Qura University Health Sciences College at Al-Leith Department of Public Health Lecture (8)

differentiation of Inverse Trigonometric functions

Objectives: 1/ Show the table of differentiation of Inverse Trigonometric functions. 2/ Apply differentiation of Inverse Trigonometric functions by using General Low.

we have

Summary Derivative Function sin-1x cos-1x tan-1x cot-1x sec-1x csc-1x

Find dy/dx if y = x2 tan-1x Solution : dy/dx = x2 + tan-1x (2x) Example Find dy/dx if y = x2 tan-1x Solution : dy/dx = x2 + tan-1x (2x) = x2 + 2x tan-1x

Find dy/dx if y = x sin-1x Solution : dy/dx = x + sin-1x (1) Example Find dy/dx if y = x sin-1x Solution : dy/dx = x + sin-1x (1) = x + sin-1x

Find dy/dx if y = sinx tan-1x Solution : dy/dx = sinx + tan-1x (cosx) Example Find dy/dx if y = sinx tan-1x Solution : dy/dx = sinx + tan-1x (cosx) = sinx + cosx tan-1x

Find dy/dx if y = 3x sec-1x Solution : dy/dx = 3x + sec-1x (3) Example Find dy/dx if y = 3x sec-1x Solution : dy/dx = 3x + sec-1x (3) = 3x + 3 sec-1x

b. y = sin-1x . tan-1x C. y = x ln(x) + 5cot-1x Exercise Find dy/dx for the following functions a. y = cos-1x / ex b. y = sin-1x . tan-1x C. y = x ln(x) + 5cot-1x

Thanks Radia