1. Use the power rule to differentiate. a) f(x)=x\" b) f(x)=x c) f(x)=xv'5 d) 10(35):)? 9)f(x)=x5 016(16):? 2. Differentiate. 2f3x a) f(x)=23x+4x3 b) f(x)=3(2x+1)2 c) f(x)= d) f(x) = J? 3. Find the equation of the tangent line at the point P(2,4) to the graph of y = f (x) = x3 2x. 4 4. Find the point(s) on the graph of y = f (x) = x + 2 where the tangent line is horizontal. x 2 5. Find the point(s) on the graph of y = f (x) = where the slope of the tangent line equals 8. x 6. Find the equation of the normal line to the curve y = f(x) =1+ 1/23: at P(2,3). 1. Use the product rule to differentiate. Do not simplify. a) f(x) = (x2 1)(x3 + 2x) b) f(x) = (J2 \"xi/272\"!) 2. Use the product rule to differentiate. Do not simplify. a) ftx) = $0: 2m:2 + x) b) f(x) = (x +1)(x2 2x)(x3 + 4x2) 3. Find f'(1) where f(x)=(J +1)[;;2 +1]. x 4. Find the equation of the tangent line at the point P(l,2) to the graph of y = f(x) = (2x3 x2)(x2 3x) . 5. Use the generalized power rule (Chain Rule) to differentiate. Do not simplify. 10 a) f(x)=(x42x+1)7 b) f(x)=[f_3] x 6. Use the product and the generalized power rules (Chain Rule) to differentiate. Simplify the answer. f(.1i:)=(x2 2x +1)4(2x3 3)3 7. Differentiate. Simplify the answer. f(x) =1:2 Jx1 1 . Use the quotient rule to differentiate. Write the answer in a simplified factored form. 2 a) x): x b) f(x)='/2;+1 x+l x 1 2. Use the quotient rule and the generalize power rule (chain rule) to differentiate. Write the answer in a simplified factored form. 3 _ 3 a) ftx)=("+2) to feel" 1) (36-1)2 x+1 3. Find the slope of the tangent line to the curve = at the point P(2,l) . 3' 3 x x+2 x2 4x x2+2 4. Find the point(s) where the tangent line is horizontal for the curve y = r2(t+1)3 r2+l 5. Given the position function s(t) = , find the velocity at t=1 . 1. If u = x2 + 1 and v= Vu , find dy dx 2. If u = - and v = - u - 1 dv x u + 2 , find dx =1 3. Use the chain rule to differentiate. Write the answer in the simplified and factored form. f ( x) =x (x2 - x+1)+ 4. Evaluate f' (2) if f (x) = x3 x-1 Vx2 + 1