Dear Tutor, Kindly provide me the answer with explanation, so that i will be more understand. Please show step by step for every calculation. Thank you in advance.

Course: Calculus I

Topics : 1. Differentiation using the definition of derivative 2. Differentiation using formula/rules

TABLE OF INTEGRALS APPENDIX 1 ax + b)"+1) RULES OF DIFFERENTIATION -+C; n*-1 1 . ( ax + b ) " dx = a(n + 1) 1. Product rule - Inlax + b + c ; n=1 (f ( x )9 ( x) ) = g(x )f' ( x) + f ( x ) g ' ( x ) a 2. Quotient rule 2 . [4dx = In/x] + C d f(x) g(x) f'(x) -f(x) g'(x) dx g(x) (g(x))2 3 . sin axdx = - -cos ax + C 3. Power rule 4. cos axdx = - sin ax + C - ( 1( x ) " = n[f( x ) / " - ' f ( x ) 5 . sec 2 axdx = - tan ax + C 4. Chain rule dx "f (g ( x) ) = f' (g(x)) g'(x) 6 . csc2 axdx = - -cot ax + C a DEFINITION OF DIFFERENTIATION f'(x) = lim f ( x + h)-f(x) h-+0 hDEFINITION OF DIFFERENTIATION Question 1 f'(x) = lim f( x + h)-f(x) h-+0 h Find f'(x) using the definition of the derivative for a) f (x) = 2x2 + 3x b) f (x ) = Vx+ 1 3 c) f (x ) = x +6 15 MarksAPPENDIX 1 Question 2 RULES OF DIFFERENTIATION 1. Product rule " (f ( x )9 (x )) = g(x)f' ( 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 Of (g (x) ) = f'(g(x)) g'(x) Find f'(x) using the appropriate formula : a) f(x) = 5x7 - 3x5 + Vx+ 10x+8 b ) f (x) = (3x4 - 7x3)5 c) f (x) = (5x + 3) (8x - 3)4 3x - 6 d) f (x ) = x2 + 3x - 7 20 MarksQuestion 5 Find the derivative the equation of a tangent line to the function f(x) = x3 +3x2 - 2x + 3 atx = 1 andy =5 5 Marks