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

2024
Views:

151

Pages:

3
Author:

Jalen W.

Instructor: Neelam Aggarwal Course: Spring 2022 - Calculus I (MATH1441-02F) Student: Jalen Wilson Date: 07/12/24 Assignment: Section 3.3 Enhanced Assignment 1. Find the indicated derivative. dy 3 if y = 7x dx dy 2 = dx 21x 2. Find the indicated derivative. f′(x) if f(x) = 3x + 5 x The derivative of the function f(x) = 3x + 5 x is 5 3− 2 x . 3. Differentiate the function and find the slope of the tangent line at the given value of the independent variable. 3 2 s = t − 4t , t= −7 2 s′(t) = 3t − 8t The slope of the tangent line is 203 at t = − 7. 4. Find the value of the derivative. dy 2 if y = 1 − 5x dx x = − 3 dy = dx x = − 3 30 (Simplify youranswer.) 5. Find the first and second derivatives. 3 s = 6t − 3t ds = dt 6 2 18t − 18t 2 d s dt 2 = 36t − 90t 5 4 6. Find the first and second derivatives. 5 y= dy 7x 5 − 2x + 3e 4 = 7x − 2 + 3e dx 2 d y dx 2 = 3 x 28x + 3e x x 7. Find the derivative of the function. y= 5x − 7 4x + 9 The derivative is y′ = 73 (4x + 9) 2 8. Find the derivative of the function. 2 y= 4x + 9 2 x +2 y′ = 2x − 2 2 x +2 9. Find the derivative of the function. y = 4e dy dx −x = − 4e +e −x 3x +e 3x •3 10. Find the derivative of the function. 2 y = x ex 2 y′ = 2x • e + e • x x x 11. Find the derivative of the function. 5/4 y=x + e− 3x 1 dy dx = 5x 4 − 3e 4 − 3x 12. Find the derivative of the function. s = 5t ds dt 6/5 + 4e 2 1 = 6t 5 13. Find the derivative of the function. r= dr dw 5e w 9w w = 5we − 5e 9w 2 w . 14. Find the derivative of all orders of the function. x y= 4 4 + 8 3 2 x − x + 2x − 9 9 2 8x 3 y′ = x + 2 y′′ = 3x + y′′′ = y y (4) (5) − 2x + 2 3 16x 3 6x + = 6 = 0 −2 16 3 15. Suppose u and v are functions of x that are differentiable at x = 0 and that u(0) = − 4, u′(0) = 9, v(0) = − 7, and v′(0) = 2. Find the values of the following derivatives at x = 0. a. b. c. d. d dx d (uv) u d dx (uv) = d u dx v dx d v v d v dx u dx d u d dx (6v − 8u) dx = = (6v − 8u) = − 71 − 55 49 55 16 − 60