The given example should be the format of the solution:

The given example should be the format of the solution: Rules for Differentiation The process of finding the derivative of y=f(x) by using the definition of a derivative is time-consuming and tedious. The following are the standard formulas called differentiation formulas or differentiation rules which enable us to find the derivative of a complicated function as rapidly as we can write. In the formulas below, u and v are differentiable functions of x, n is any real number and c is a constant. D1 " (c ) = 0 The Constant Rule dx D2 The Identity Function Rule (x) = 1 dx D3 d ( cu) = 'dx du dx D4 d du dv The Sum Rule dx (utv) = dx+ dx D5 d du du The Product Rule dx -(uv) = u vax D6 du du The Quotient Rule d dx D7 d -(u") = num-1. du The Power Rule dx dx D8 du= du/ dx 2vu D9 -n du un+l dx Example 1. Find #% if y = 3x3 + 4x3 + 6x + 2. Solution: dy d dx dy (3x3 + 4x2 + 6x + 2) = 3- (x 3) + 4- (x2) + 6-# (x) +2 dy = 3.3 (x3-1) +4 .2(x2-1) + 6(1) +0 dx dx ay = 9x2 + 8x +6 Example 2. If y = v5x + 2, find Solution: dy = v5x + 2 dx (5x + 2) dx 2v5x + 2 dy 5 dx 2v5x + 2 B. Evaluate the following functions using the rules for differentiation 1. y = Vx + + Vx 2. y = V5 - 6x 3x+1 3. y = V3x2+2 4. y = (3x + 4)2(x -5)3 5. y = (4x+1)3