Chain Rule 4

More Derivatives Using Tables EX #4: Let f (x) be a continuous and differentiable function on the interval O < x < 1, and let g(x) = f(4x). The table below gives values of f'(x), the derivative of f(x). Find the value of g' (0.2). X 0.1 0.2 0.4 0.5 0.6 0.7 f'(x) 0.75 0.823 0.964 1.033 1.081 1.104 9Cx)-{ {4x) g'(x)-:::f '( 4rl · (4 l 9 '(0,~ )~+'[4(0,:l)J' 4 9 1 { O:l) =- .f 'Co. 8 ) • 4 9 '((),l):: (\ J lSH4) 9 >(O,ll= '-l. 5 EX #5: Use the table below to complete the following. l ' - x· f(x) f'(x) g(x) -1 -2 4 -1 0 4 3 2 2 3 -2 -4 r , 8. If J(x) = f,(g(x)) • cosx, what is the value of}'(0)? j')(x)=4'(9Ct)) (9 1 00) (OS}(;-{ (9(x))(-si,n1 0 1'(0):..f'{9(0)) t9CoJ)(c.oso) t { --· J") ( (J) .f l C 2 ){ - 3 l ( I ) • J •co)-=- (-1)( 3)l 'I) J'(o)-=-~ g'(x) 2 -3 1 0.8 1.125 t 4