Quotient Rule & Chapter 3.3 Derivatives of Trigonometric Function Notes - Edubirdie

University:
York University
Course:
MATH 1013 | Applied Calculus I
Academic year:

2022
Views:

78

Pages:

4
Author:

Nick T.

Quotient Rule y = f(x)/g(x) => y' = (g(x)f'(x) - f(x)g'(x)) / (g(x))^2 Examples: y = (x^2 + 4x + 3) / (x^2 + 1) => y' = (2x + 4)(x^2 + 1) - (x^2 + 4x + 3)(2x) / (x^2 + 1)^2 y = (3^x * ln(x)) / x => y' = (3^x * ln(3) * x + 3^x * (1/x) - 3^x * ln(x)) / x^2 3.3 Derivatives of Trigonometric Functions How to graph trig functions y = sin(x) (tan(x))' = (sin(x)/cos(x))' = (cos(x)cos(x) - sin(x)(-sin(x))) / (cos(x))^2 = (cos^2(x) + sin^2(x)) / (cos^2(x)) = sec^2(x) (sin(2x))' = cos(2x) * 2 (cos(x))' = -sin(x) (tan(x))^5 = (sin(x)/cos(x))^5 = (sin^5(x))/(cos^5(x)) Derivatives of Trigonometric Functions f(x) f'(x) sin(x) cos(x) cos(x) -sin(x) tan(x) sec^2(x) sec(x) sec(x)tan(x) csc(x) -csc(x)cot(x) cot(x) -csc^2(x)

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