Homework Help is Here – Start Your Trial Now!
Math
Calculus
Preview Activity 5.4.1. In Section 2.3, we developed the Product Rule and studied how it is employed to differentiate a product of two functions. In particular, recall that if ƒ and g are differentiable functions of x, then a. For each of the following functions, use the Product Rule to find the function's derivative. Be sure to label each derivative by name (e.g., the derivative of g(x) should be labeled g'(x)). d -[ƒ(x) · g(x)] = f(x) · g'(x) + g(x) · ƒ'(x). dx i. g(x) = x sin(x) iii. p(x) = x ln(x) v. r(x) = e* sin(x) b. Use your work in (a) to help you evaluate the following indefinite integrals. Use differentiation to check your work. İ. ·[re² [2.r cos iii. V. xe te dữ 2x cos(x) — x² sin(x) dx 1 + ln(x) dx ii. h(x) = xe* iv. q(x) = x² cos(x) ii. iv. [e² (sin(x) + cos(x)) da [r cos(x) + sin(x) da

Preview Activity 5.4.1. In Section 2.3, we developed the Product Rule and studied how it is employed to differentiate a product of two functions. In particular, recall that if ƒ and g are differentiable functions of x, then a. For each of the following functions, use the Product Rule to find the function's derivative. Be sure to label each derivative by name (e.g., the derivative of g(x) should be labeled g'(x)). d -[ƒ(x) · g(x)] = f(x) · g'(x) + g(x) · ƒ'(x). dx i. g(x) = x sin(x) iii. p(x) = x ln(x) v. r(x) = e* sin(x) b. Use your work in (a) to help you evaluate the following indefinite integrals. Use differentiation to check your work. İ. ·[re² [2.r cos iii. V. xe te dữ 2x cos(x) — x² sin(x) dx 1 + ln(x) dx ii. h(x) = xe* iv. q(x) = x² cos(x) ii. iv. [e² (sin(x) + cos(x)) da [r cos(x) + sin(x) da

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
See similar textbooks
icon
Related questions
Question

Only need help with a and b please, thank you!

Preview Activity 5.4.1. In Section 2.3, we developed the Product Rule and studied how it is employed to differentiate a product of two functions. In particular, recall that if f and g are differentiable functions of x, then a. For each of the following functions, use the Product Rule to find the function's derivative. Be sure to label each derivative by name (e.g., the derivative of g(x) should be labeled g'(x)). i. d -[ƒf(x) · g(x)] = f(x) · g'(x) + g(x) · ƒ'(x). dx i. g(x) = x sin(x) iii. p(x) = x ln(x) v. r(x) = e* sin(x) b. Use your work in (a) to help you evaluate the following indefinite integrals. Use differentiation to check your work. iii. V. xe te da [2x [1+ 1 + ln(x) dx ii. h(x): =xe* iv. q(x) = x² cos(x) 2x cos(x) — x² sin(x) dx ii. iv. e* (sin(x) + cos(x)) dx [x x cos(x) + sin(x) dx c. Observe that the examples in (b) work nicely because of the derivatives you were asked to calculate in (a). Each integrand in (b) is precisely the result of differentiating one of the products of basic functions found in (a). To see what happens when an integrand is still a product but not necessarily the result of differentiating an elementary product, we consider how to evaluate
Transcribed Image Text:Preview Activity 5.4.1. In Section 2.3, we developed the Product Rule and studied how it is employed to differentiate a product of two functions. In particular, recall that if f and g are differentiable functions of x, then a. For each of the following functions, use the Product Rule to find the function's derivative. Be sure to label each derivative by name (e.g., the derivative of g(x) should be labeled g'(x)). i. d -[ƒf(x) · g(x)] = f(x) · g'(x) + g(x) · ƒ'(x). dx i. g(x) = x sin(x) iii. p(x) = x ln(x) v. r(x) = e* sin(x) b. Use your work in (a) to help you evaluate the following indefinite integrals. Use differentiation to check your work. iii. V. xe te da [2x [1+ 1 + ln(x) dx ii. h(x): =xe* iv. q(x) = x² cos(x) 2x cos(x) — x² sin(x) dx ii. iv. e* (sin(x) + cos(x)) dx [x x cos(x) + sin(x) dx c. Observe that the examples in (b) work nicely because of the derivatives you were asked to calculate in (a). Each integrand in (b) is precisely the result of differentiating one of the products of basic functions found in (a). To see what happens when an integrand is still a product but not necessarily the result of differentiating an elementary product, we consider how to evaluate
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS