2. Trying out derivatives rules We have learned the following rules for calculating derivatives without going through the analysis of average rates of change: Constant rule: the derivative of a constant function is 0. Power rule: the derivative of x" (considered as a function of x) is nx*=1. Constant multiple rule: If you multiply a function by a number, its derivative gets multiplied by the same number. Sum rule: the derivative of a sum of two functions is the sum of the derivatives. a. Calculate g'(x), where g is the function defined by g (x) = 1.1x? - 5x + 11. b. Calculate h'(x), where h is the function defined by h(x) = x7 - x - 1.Homework 10 1. Let p be the function defined by p(x) = sin(x). That's the sine function evaluated at x; in calculus class, we always use radians for our trigonometric functions. Before you continue, check that your calculating tool is using radians: sin (1) should be 0.8414709848. if you get 0.01745240644 instead, you need to switch from degrees to radians. Please read my solutions for Homework & before answering the first three questions below. a. Complete the following table, which you will use to estimate p'(1). Be very careful about rounding. If you round values anywhere, your numbers in the last column will not make sense. 1+h p(1 + h) (p(1 + h) = p(1)] 0,01 0.001 0.0001 0.00001 b. Judging from the numbers in the table, what is your best estimate of p'(1)? C. How many decimal places in your estimate of p'(1) are you confident are correct? Explain your thinking using what you see in the table