QUESTION 3 Given that f(x) =57x , use the definition of derivative to find f'(x). Simplify your answer. (5 mark QUESTION 4 Find dy dx using appropriate differentiation techniques. a) xlny xy2 =5+ Vin(x?)+1. (4 mark b) y = sin?(sin2x)- sin(x +1) (3 mark 2 DEFINITION OF DIFFERENTIATION f'(x)= lim f(x+h)-f(x) no h LINEAR APPROXIMATION f(x)=f(xo)+f'(xo Xx-xo) SIGMA NOTATION 1. ak = a1 + a2 + az +...+ an k=1 n 2. n(n+1) k= 1+2+3+...+ n= 2 k=1 n 3. +32 k2 = 12 +2 +32 + ... + n2 = n(n+1) (2n +1) 6 k=1 n 4. k = +2 + 3 +...+ n = n(n+1)] 2 k=1 THE SECOND FUNDAMENTAL THEOREM OF CALCULUS g(x) d jro)dt = f(g(x)g(x) d x a