if f (x) = In (2x + 1) So the 4th derivative is f ( 4 ) ( I ) = here is y = 202-2x . 323 -3x2 .74x+4 Apply the In function to both sides, then simplify with the help of the laws of logarithms. a) For what values of A , B , C and D can we write In (y) = In (A) x3 + In (B) z2 + In(C) z+ In (D)? A = B = C = D = b) Derive the value of the derivative at 0, using implicit differentiation. Answer y', when x=0, is; Evaluate In (3 + h) - In (3) lim h-+0 hAnswer= Determine the equation of the tangent to the curve y = 5 In 24 e23 at point (1.5). (Hint: simplify before taking the derivative.) Express your answer as y= mx+b which one is for which: -- V d cot(I) - V darctan(x) -- V tan(x) darcsin(x) - V dsec(I) d -arccos(I) d csc(I) 1. tan(x) sec(x) 2. 1+22 3. VI-22 -1 4. VI-22 5. - csc () 6. sec2 (z) 7. - cot(r) csc(z)if f(x) = 2 +2 arcsin(x) evaluez f' (0) 5 cos (I) f' (0) = Let the function f(x) = (arctan(x))+ 4arctan(x) + 6. What is the derivative of f(x)? Let the function g(x) = arcsin(e 47) + 3. What is the derivative of g(x)? The function y is implicitly given by the equation y? In(y) - x4 In(z) =7 Find the derivative of y as a function of x and y y'=We consider the ourve of the equation Along this ourve {except at a few points]: 3! is an implicit function of x a} Determine the derivative dyfdx as a function of x and y