Calculus AB Independent Study Chain Rule Practice Study Sheet 4. For each of the following, find dy A. y = (x2+3)6 B. y = V2x-3 - 7x C. y = 2tan(-5x-2) 5. Suppose f is a differentiable function of x. Use the chain rule to prove each of the following. A. If fis an odd function, f (x) is an even function. B. If f is an even function, then f (x) is an odd function. 6. Suppose f and g are differentiable functions of x on the domain of all real numbers. The table below gives some values for the functions and their derivatives at a few values of x. x f(x) f (x) 8(x) 8'(x) -2 -2 0 - 2 0 2 5 2 4 -2 4 -2 -4 A. If h = fog, what is the value of h'(2)? B. If h = fof, what is the value of h'(4)? C. If h(x) = f(x3 + 1), then what is the value of h'(1)? D. If h(x) = g(x) , what is the value of h'(-2)? 7. For each of the following, find dy A. y = sin2(cos(3x-2)) B. y = 1+ /1+ Jx C. y = tan( (x+ 4 ) 7 , 8. Complete the questions below. A. Find the 100th derivative of sin(3x). (Hint: Find the pattern here.) B. If y = 4sec(3x -3 - 1) + , what is the derivative of y with respect to (3x-3 - 1)