University:
Georgia Southern University
Course:
MATH 1441 | Calculus I
Academic year:

2024
Views:

214

Pages:

4
Author:

Jalen W.

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/12/24 1. Given y = f(u) and u = g(x), find 1 y = 6u − 1, u = dy dx 2. 3 dy dx = f′(g(x))g′(x). 7 x 6 = 14x Given y = f(u) and u = g(x), find dy dx = f′(g(x))g′(x) for the following functions. y = sin u, u = 5x − 2 dy dx 3. = f′(g(x))g′(x) = 5 cos (5x − 2) Given y = f(u) and u = g(x), find y= dy dx 4. 4 = − dy dx = f′(g(x))g′(x). u , u = cos x sin x 4 3 4 cos x Given y = f(u) and u = g(x) below, find dy dx = f′(g(x))g′(x). y = 3 sin u, u = 6x − 6 cos x dy dx = 3 cos (6x − 6 cos x) • (6 + 6 sin x) 5. Findf(x) andg(x) such that h(x) = (f ◦ g)(x). h(x) = (1 − 6x) 2 Suppose that g(x) = 1 − 6x. f(x) = 6. 2 x Given y = f(u) and u = g(x), find dy dx = f′(g(x))g′(x) for the following functions. y = tan u, u = 13x + 3 dy dx 2 = f′(g(x))g′(x) = 13 sec (13x + 3) Assignment: Section 3.6 Enhanced Assignment 7. Write the function below in the form y = f(u) and u = g(x), then find dy dx as a function of x. y = cos ( tan x) What are the functionsf(u) andg(x)? f(u) = cos u g(x) = tan x Determine dy dx 8. dy dx . 2 = − sin ( tan x) sec x Write the function in the form y = f(u) and u = g(x). Then find y=e dy dx as a function of x. − 19x Which of the following has the function in the form y = f(u) and u = g(x)? A. y = − 19u, u = e x u B. y = − e , u = 19x u C. y = e , u = − 19x D. y = 19u, u = e dy Find dy dx 9. dx = −x . − 19e − 19x Write the function in the form y = f(u) and u = g(x). Then find y=e 1 − 2x Choose the correct form of y in terms of u. A. y = eux , where u = 1 − 2 B. y = e− 1 + 2u , where u = − x C. y = u1 − 2x , where u = e D. y = eu , where u = 1 − 2x dy dx = − 2e 1 − 2x 10. Find the derivative of the function y = dy dx = 9 2 − 5 + 9x − 5 + 9x . dy dx as a function of x. 11. Find the derivative of the function. q= 4 3 x + 2x 2 3x + 2 q′ = 3 4 3 4 x + 2x 12. Find the derivative of the function y = (cot x − csc x)− 1 . dy dx = − csc x cot x − csc x 13. Find the derivative of the function. f(x) = 5 + x tan x 2 d 5 + x tan x = dx x sec x + tan x 2 5 + x tan x 14. Find the derivative of the given function. y = cos e dy dθ 15. = 4θe Find dy dt − 2 θ2 − 2 θ2 sin e . y = (t tan t) dy dt 16. = 8(t tan t) Find dy dt dt 17. 8 7 2 t sec t + tan t . y = tan dy 5 2 sin t 4 2 2 5 = 10 sin t sec Find dy dt dt = 5 sin t tan . y = 3t 2t − 5 dy − 2 θ2 2 2t − 5 4 2 66t − 15 5 sin t cos t 18. Find y′′ for y = 3 + y′′ = 3 4 . x − 24(3x + 4)( − 3x − 8) 5 x 19. Find y′′. y = x(3x + 4) 3 4 2 y′′ = 1620x + 5184X + 5184X + 1536 20. Find the tangent to y = ((x − 3) / (x + 2))2 at x = − 1. y = − 40x − 24 (Type anequation.)