Let y = 372-4x 423 -5x2 72x+4 a) Given that In (y) can be written in the form In (y) = In (A) " + In (B) r + In (C) r+ In (D). What are the coefficients A, B, C, and D ? A = B = C = D = dy b) Using the correct answer to (a), and implicit differentiation, find the value of when = = 0. Answer:Find the equation of the tangent line to the curve y = 2 1n 3 I' e' at the point (1, 2) . (Hint: simplify before differentiating.) Your answer must be an equation of the form y = mr + b This question accepts equations. E.g. y-2 = 5(x-4)+1.\fEvaluate In (3 + h) - In (3) lim h-+0 h This question accepts numbers or formulas.Consider the function f(x) = 4arcsin(x) arccos(x) - 6arctan(I). What is the derivative of f(x) at x = 0? f' (0) = FORMATTING: Your answer should be exact. Remember to write symbols like * and : I as pi and sqrt(x) , respectively.Match the following numbered functions with their derivatives: -sec (E) cot( I) d csc(I) di -arctan(I) d -arccos(I) tan(I) d arcsin(I) 1. - csc (I) 2. - cot(I) CSC(I) 3. tan(I) sec(I) -1 4. V/1-12 1+12 6. sec () 1 7. 1-12Consider the function f(z) = (arctan(x))# + 3arctan(x) +6. What is the derivative of f(I)? FORMATTING: In Mobius, arctan(x) is written arctan (x). Answer: f (=) =