Differentiation Questions and Answers

Tutorial Exercise Find the derivative of the function 4x 6x f x Step 1 The function f x can be simplified to make the algebraic process of finding the derivative easier f x 4 6

Find the given higher order derivative f 3 x x8 f 4 x f 4 x x x8 f x Your answer cannot be understood or graded More In

Find an equation of the tangent line to the graph at the given point The graph is called a Witch of Agnesi y 2 y 6 2 f x 5 x 1 2 1 2

Function f x tan x Point a Find an equation of the tangent line to the graph of the function at the given point Let x be the independent variable and y be the dependent variable b Use a graphing utility to graph the function and its tangent line at the point y R A KIN C YX AUX O O A

Find an equation of a line that is tangent to the graph of f and parallel to the given line Function Line f x x 3x y 8 0 y 11 y 11 smaller y intercept larger y intercept

The tangent line to the graph of y g x at the point 5 2 passes through the point 8 6 Find g 5 and g g 5 g 5

Find the derivative of the function using the definition of derivative f x x 9x 1 f x 11 State the domain of the function Enter your answer in interval notation State the domain of its derivative Enter your answer in interval notation

a f 0 b f 1 c f 2 d f 3 e f 4 f f 5 g f 6 h f 7 YA 1 0 1 y f x X

Find the derivative of the function using the definition of derivative g x 7 x g x State the domain of the function Enter your answer using interval notation State the domain of its derivative Enter your answer using interval notation

y I Show Transcribed Text 2 RISE rea of the inscribes polygon or circumscribed indicated

Find the sum 2 5 12 9 7n

Simplify the following rational expression Give your answer as a reduced rational expression x 2x 3 x 1

Express the following with rational exponents

You are given the sample mean and the population standard deviation Use this information to construct the 90 and 95 confidence intervals for the population mean Interpret the results and compare the widths of the confidence intervals From a random sample of 61 dates the mean record high daily temperature in a certain city has a mean of 85 15 F Assume the population standard deviation is 13 94 F The 90 confidence interval is Round to two decimal places as needed

Find all the second order partial derivatives of the following function W 4x 2y 2 2x 2y

7e7x e7x 2 This can be transformed into a basic integral by letting Consider the indefinite integral u du and du Te dx Performing the substitution yields the integral da