University:
Missouri State University
Course:
MTH 136 | Precalculus 1
Academic year:

2023
Views:

218

Pages:

21
Author:

Braedon Harvey

WARM-UP DIRECTIONS: Find the point(s) on the graph of f(x) where the slope of the tangent line, m, is given. 1.) f(x) = 6sqrt(x) m = 3 2.) f(x) = - 18/x m = 2 SECTION 7 Derivatives of Trigonometric Functions How can we find the derivatives of all six trigonometric functions? What are the shortcuts for all 6 trigonometric functions? RECIPROCAL DERIVATIVES: Cotangent What is the derivative for the cotangent function? COS X sin x REMEMBER: cot x f(x) = cotx = cosx hi 10 Sinx lo deh. (sinx)2 102 f'(x)=-sinx-cos²x--(sinx+cosx)=--=-(5x)=-(coxx)=-(sex S Sinx Sin²x Sin²x hi delo こ f(x) = cotx f'(x)=(sinx) (sinx)-(ask)( f'(x) = -csc²x EXAMPLE 1: Derivatives of Trig Functions f(x) = 7x ^ 2 * sin(x) f' * (x) = 7x ^ 2 * (cos x) + sin x * (i4x) f' * (x) = 7x ^ 2 * cos x + 44x * sin x f' * (x) = 7x(x * cos x + 2sin x) EXAMPLE 2: Derivatives of Trig Functions g(x) = (cot(x))/(6x ^ 3) matrix g^ prime (x)=& 6x ^ z * (- c * x ^ 2 * x) - cot x * (i / (x ^ 2)) (6x^ 3 )^ 2 aligned g^ 2 (x)=-6x^ 3 cos 3x-(8x^ 2 cotx 36x ^ 6 = (- 6x ^ 2 * (x * alpha ^ 2 * x + 3c * dx))/(36a ^ 6) \\ =- (x alpha^ 2 x alpha^ 2 +3cdx) 6x^ 4 \\ =- (x alpha)^ 2 +3cdx) 6x^ 4 aligned