MTH 171 Lecture Notes - Lecture 15: Inverse Trigonometric Functions
Document Summary
3. 10 derivatives of inverse trig functions notes: sterling. Provide a generalization to each of the key terms listed in this section. Example d dx (cid:2)sin 1 (x)(cid:3) = d dx (arcsin (x)) = 1 x2 d dx (cid:2)sin 1 (2x)(cid:3) du (arcsin (2x)) d. = d du (arcsin (u)) d dx (2x) 2 1 4x2 d dx (cid:2)cos 1 (x)(cid:3) = d dx (arccos (x)) = . 1 x2 d dx (cid:2)cos 1 (3x)(cid:3) du (arccos (3x)) d. 1 d dx (cid:2)tan 1 (x)(cid:3) = d dx (arctan (x)) = 1 x2 + 1 d dx (cid:2)tan 1 (4x)(cid:3) du (arctan (4x)) d. = d du (arctan (u)) d dx (4x) = 1 u2+1 (4(1)x1 1) 16x2+1 d dx (cid:2)csc 1 (x)(cid:3) = d dx (arccsc (x)) = . Arcsec d dx (cid:2)sec 1 (x)(cid:3) = d dx (arcsec (x)) = Example d dx (cid:2)csc 1 (5x)(cid:3) du (arccsc (5x)) d. = d du (arccsc (u)) d dx (5x)
