using the definition of derivative, find the derivative of each function: (i)f(x) = V3 -5x (ii) f(@) = : 3+x 1-3r (ini) f(x) = 23+ (iv)f(x) = zi (v)f(x) = tan r + cot r Find values of a and b that make f(x) = ax + b if x 1 not differentaible. Determine whether or not f'(0) exists if I' sin - if x # 0 if x = 0 Differentiate each function with respect to r (iy = Hr-3 (ii)y = (x+ x)3 (iii)y = (x3 - 2x)(2.x5 + 5) (iv)y = (2x+9)(323-1) (v)y = V3+6 (4+23)3 Find the derivative of each function with respect to r, simplifying your answers where possible. (i)f(x) = sin(tan vsin x) (ii) f(x) = 1 sin 1+cos vi (iii) f (x) = sec3(4x + 2) (iv) f(x) = cosec(4x + 2)3 (v) f(x) = cos 3r sin' Ar (i) If 2x2 + 6xy + 4y2 = 3, find # in terms of a and y, and show that 4 = 3 (3r+4y)3 (ii) If y = sin(sin x) prove that 14 + tanI rdy + ycos' r = 0 A curve is given parametrically by 1-21: 1 = 1+21 1-1