et f (x), g (x), h (x) be differentiable functions. Suppose g(x) is invertible. iven that f (2) = -, g(1) = 2, h (2) = 0 and f' (2) = 1, g (1) = 3, h' (2) = -1, %3D g' (2) h (x) f (x) ompute the derivative of at x = 2. Here g1 (x) is the inverse function of g (x). It is NOT - g(x) D -3 D -1

3x Let f (x) Then the derivative of f is 1 + 5x A(1 + 5*) – Bx(5*) In C_ where (1 + 5×)D f'(x) A = B = C = D = I| ||||

Suppose f(x) is a continuous differentiable function. Some of the values of the function and its derivative are shown below. X -2 3 6 7 -3 f(x) 4 F'(x) 6 0 2 (a) Let g(x) = f($). . Find g'(x). Og'(x) = -(2/2) (²) Og'(x) = ($)F($) Og'(x) = -6f'() Og'(x) = ($) f'( ) Og'(x) = f'( =) Now find g'(3) 2 -2 -5 4 3 = (b) Find the equation of the tangent line to f(x) at x = 1. Use y as the dependent variable. Now approximate f(7) =

Compute the derivative function f' (x) algebraically. f (x) = -5x3 +7 O f' (x) = -15x O f' (x) = -15z² O f' (x) = 8 – 15z? O f' (x) = 15z2 %3D