Learning activity derivatives

MAC 2311 Learning Activity #6 Name: Diff., Prod., & Quot. Rules; Derivatives of Trig. Functions Group #: 1. Prove the derivative rule of f (x) = cot(x) d cot(x) = − csc2 (x) dx by using the quotient rule. Use derivative rules to find the derivatives of the following functions. Simplify by combining like terms and canceling common factors. 3 7 + 3t 2. f (t) = (7 + t ) √ 3 t 3. r(θ) = sin θ 1 + csc θ Page 1 of 3 MAC 2311 Learning Activity #6 Diff., Prod., & Quot. Rules; Derivatives of Trig. Functions 4. Find an equation of the line tangent to the function g(x) = 2x sin x at x = 3π . 2 5. Suppose there exists a function, f (x), such that f (1) = 5 and f 0 (1) = 4. f (x) Let h(x) = . Find the equation of the tangent line to h(x) at x = 1. x+1 3 6. Find the third derivative of f (t) = 4t3 − 5 t Page 2 of 3 MAC 2311 Diff., Prod., & Quot. Rules; Derivatives of Trig. Functions Learning Activity #6 7. Find the 42nd and 55th derivative of f (x) = cos x. 8. Use this table to find the following: x f (x) g(x) f 0 (x) g 0 (x) 2 3 2 3 7 3 5 7 3 -2 4 4 -1 -1 1 5 3 2 -2 8 d (a) − 2f (x) dx x=5 d 2 (b) x f (x) dx x=3 (c) Find the equation of the tangent line to y = g(x) at x = 4. f (x) Page 3 of 3