ECET2e Section 2.5 21/10/2016, 02:27 WebAssign ECET2e Section 2.5 (Homework) Current Score : 0 / 15 Thu Aung MATH-UA 121, section 11, Fall 2016 Instructor: Benjamin Harrop-Griffiths Due : Thursday, October 20 2016 05:00 PM EDT 1. -/1 pointsSEssCalcET2 2.5.012. Find the derivative of the function. f(t) = 5 3 + tan t f'(t) = 2. -/1 pointsSEssCalcET2 2.5.014. Find the derivative of the function. y = a6 + cos6 x y'(x) = 3. -/1 pointsSEssCalcET2 2.5.021. Find the derivative of the function. y= x2 + 1 5 x2 1 y' = https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=14686157 Page 1 of 5 ECET2e Section 2.5 21/10/2016, 02:27 4. -/1 pointsSEssCalcET2 2.5.025. Find the derivative of the function. y= r r2 + 2 y' = 5. 0/1 points | Previous AnswersSEssCalcET2 2.5.029. Find the derivative of the function. y = sin(tan 8x) y' = Enhanced Feedback Please try again using the Chain Rule several times. First identify the outer function. Find the derivative of the outer function [evaluated at the inner function] and then multiply by the derivative of the inner function. In order to find the derivative of the inner function, let the previous inner function be the new outer function, identify the new inner function, and continue the same d method. In other words, f(g(h(x))) = f'(g(h(x))) g'(h(x)) h'(x). Identify f, g, and h. dx 6. -/1 pointsSEssCalcET2 2.5.035. Find the derivative of the function. y = cot2(sin ) y' = https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=14686157 Page 2 of 5 ECET2e Section 2.5 21/10/2016, 02:27 7. -/1 pointsSEssCalcET2 2.5.041. Find the derivative of the function. y = cos sin(tan 3x) y' = https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=14686157 Page 3 of 5 ECET2e Section 2.5 21/10/2016, 02:27 8. -/6 pointsSEssCalcET2 2.5.057. If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) = g(g(x)). Find each derivative, if it exists. If it does not exist, explain why. (If an answer does not exist, enter DNE.) (a) u'(1) = It does exist. u'(1) does not exist because f '(1) does not exist. u'(1) does not exist because g'(1) does not exist. u'(1) does not exist because f '(3) does not exist. u'(1) does not exist because g'(2) does not exist. (b) v'(1) = It does exist. v'(1) does not exist because f '(1) does not exist. v'(1) does not exist because g'(1) does not exist. v'(1) does not exist because f '(3) does not exist. v'(1) does not exist because g'(2) does not exist. (c) w'(1) = It does exist. w'(1) does not exist because f '(1) does not exist. w'(1) does not exist because g'(1) does not exist. w'(1) does not exist because f '(3) does not exist. w'(1) does not exist because g'(2) does not exist. https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=14686157 Page 4 of 5 ECET2e Section 2.5 21/10/2016, 02:27 9. -/2 pointsSEssCalcET2 2.5.050. (a) The curve y = |x|/ 2 x2 is called a bullet-nose curve. Find an equation of the tangent line to this curve at the point (1, 1). (b) Illustrate part (a) by graphing the curve and the tangent line on the same screen. https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=14686157 Page 5 of 5 \f