Find the equation of the tangent line to the given function at the given point. 1. f(x) = 89" + 4x: (0,8) 2- f(x) = 69" '2 - 3x2: (2, - 6) 3. f(x) = 2In(x + 3); (2,0) 4- f(X) = |n(x + 4) - 2x; (-3.6) Evaluate the derivative using logarithmic differentiation. 5- f(X) = (x + l)"(x + 3)3 Evaluate the following. 1. 8dx 2 . J - 4dy 3 . Tidx 4. S(5ex - 12 ) ax 5 . [2x + 1 - dx X 6. (2xe * + X -dx 4-7 X 7. (-144x1)dx om 8. /(-Tax m 9. (3x2 - 12x3 + 2x -1 + 3x-4)dx 10. (4x5 - x2 - X dx *2 11. ( x2 - 2) (x2 + 3) dx2. Basic rules and examples. a. Power rule Rule where C is constant [ xax = xn+1 n + 1 https://youtu.be/onwc1 M8eDM E b. Written examples. Example 1. (12x5) dx 1. Use the constant rule 12 ( x 5 ) dx 2. Recall the power rule 12 - + C 3. Simplify 2 x6 + CExample 2. 1( # )ax 1. Use the constant rule 4 / ( x - 5 ) dx 2. Recall the power rule x- 5+1 + C -5+1 3. Simplify = - + C x 4 Example 3. POWER RULE DOES NOT APPLY (x - 1) dx 1. Recall that S( )ax = Inlx/ + C S (x -1)ax = S()ax 2. Evaluate = Inlx| + CD Question 1 15 pts Find the equation of the tangent line to the given function at the given point. f(x) = 29"3 - x2; (3. - 7) D Question 1 5 pts Evaluate the following. You do not need to include +C in your response. J - 12dy D Question 2 5 pts Evaluate the following. You do not need to include +C in your response. (-120x9 )dx D Question 3 5 pts Evaluate the following. You do not need to include +C in your response. (6x2 -24x3 +2x-3+25x-5)dx ANSWER FORMAT: For negative exponents, leave them negative in your typed answer. Example. Type x^(-3) for x - 3