MATH241 Lecture Notes - Lecture 18: Trigonometric Functions
9 May 2018
School
Department
Course
Professor
MATH241 - Lecture 18 - Derivatives of Inverse Trigonometric Functions and Logarithmic
Functions
3.5: Derivatives of Inverse Trigonometric Functions
Arc Sine
→ xy =sin−1 in ys =x
Use implicit: → (cos y)y′= 1 y′=1
cos y
(Pythagorean identity)y ycos2+sin2= 1
y′=1
√cos y
2=1
√1 − sin y
2=1
√1 − x2
Arc Cosine
→ xy =cos−1 os yc =x
→ (− in y)s y′= 1
y′=1
sin y= − 1
√1 − cos y
2
Arc Tangent
→ xy =tan−1 an yt =x
→ ysec2(y)
′= 1
→ y′=1
sec y
2
y y1 + tan2=sec2
→ y′=1
1 + tan y
2=1
1 + x2
Arc Secant
→ xy =sec−1 ec ys =x
(sec y tan y)y′= 1
→ y′=1
sec y tan yy′=1
√
xsec y − 1
2=1
√
xx − 1
2
Derivatives of the Inverse Trigonometric Functions
1) sin x
d
dx
−1 =1
√1 − x2
2) cos x
d
dx
−1 = − 1
√1 − x2
Document Summary
Math241 - lecture 18 - derivatives of inverse trigonometric functions and logarithmic. Use implicit: cos2 + sin2 = 1 y y y = = x (cos y) y = 1 y = 1 cos y (pythagorean identity) ( in y) y = 1 s. = x os y c y = 1 sin y = . = x x an y t sec2 (y ) = 1. Arc secant ec y y = sec 1 x s (sec y tan y) y = 1 y = sec y tan y. 6) d dx d dx d dx d dx tan x cot x sec x. G = 1 x2 (x) ec x sec x. = (sec x tan x ) sec x. = 4x3 sec x tan x sec x. [ d dx: sec 1 3 + s. 1 3 + 3x sec x x3 x 1. 1 ( x)2 cos 1 + 1 x2 ( x.
