QUESTION 2 a) Find f' (x) for f (x) = X using the definition of derivative. 5x - 2 (5 marks) b) Given the function In (2x + 1) + y-sinx =4y +10 i) Find - using implicit differentiation. dx ii) Find the slope of the tangent line to the function at point | 0,- NIG (8 marks) c) if y = ex , show that 2x2 dy - - X =-2xy - dx (5 marks)APPENDIX 1 RULES OF DIFFERENTIATION 1. Product rule (f ( x ) 9 ( x ) ) = g(x )' ( x ) + f(x )g'(x ) 2. Quotient rule d (f (x) _ g(x) f(x)- f(x)g'(x) dx g(x) (g(x)) 3. Power rule "( f( x ) ) " = n[f( x ) ]" ' f ( x ) 4. Chain rule dx "f (g(x)) = f(9(x)) g'(x) TABLE OF INTEGRALS (ax + b)7+1) +C; n#-1 1 . [( ax + b ) " dx = a(n + 1) - Inlax + b/ + C ; n=1 2 . - dx = In/ x | + c 3 . sin axdx = - - cos ax + C 4. cos axdx = - sin ax + C 5 . sec? axdx = = tan ax + C 6. csc2 axdx = --cot ax + c a