Use the product rule to answer each of the questions below. It is not necessary to algebraically simplify any of the derivatives you compute. (a) Let m(w)=3w174. Find m'(w). m'(w) 3w174" In (4)+514216 x (b) Let h(t) = (sin(t) + cos(t))t. Find h'(t). h'(t)=sin(t) (4-4)+cos(t) (4 + 4t) (c) Determine the slope of the tangent line to the curve y = f(x) at the point where a = 1 if f is given by the rule f(x) = e sin(a). Start by determining f'(x). f'(x) e(sin(x) + cos(x)) f'(1) e(sin(1) + cos(1)) (d) Find the tangent line approximation L(x) to the function y = g(x) at the point where a = -1 if gis given by the rule g(x) = (x+x)2. g'(x) = (x +x)2x g'(-1)= 1 12 X L(x)= (x+1) 2