Trigonometric Function Derivatives (Calculus Problems and Solutions)

#TrigonometricFunctions #trigonometry #calculus

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(0:00) Verify that d/dx(sin(x))=cos(x) (use angle sum identity)
(6:41) Verify that d/dx(cos(x))=-sin(x) (use Pythagorean identity and the Chain Rule)
(10:44) Find second derivative of sine and cosine
(12:14) Graphical interpretation of the results
(14:34) Find the 31st derivative of sin(x)
(15:48) Derivatives of tangent and cotangent (tan(x) and cot(x))
(18:51) Derivatives of secant and cosecant (sec(x) and csc(x))
(20:37) Derivative of e^(-2t)cos(3t)+e^(-2t)sin(3t) (Linearity, Product Rule, and Chain Rule)
(23:11) Derivatives of e^(sin(x)) and sin(e^(x)) (Chain Rule)
(24:15) Derivative of cos^2(x)+sin^2(x) (Chain Rule)
(25:05) Where is cos(x^2) an increasing function? (first positive interval)
(29:03) Sinusoidally varying population word problem
(35:17) Period of an oscillating mass in terms of the mass m and spring stiffness constant k

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