Stephanie Townsend Home H Courses Week 6 "The Chain Rule and Implicit Differentiation" Take Test: W6 Quiz Take Test: W6 Quiz Test Information
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Multiple Attempts Not allowed. This test can only be taken once.
Force Completion This test can be saved and resumed later. QUESTION 1 4 points Save Answer Find the derivative of the function. r = (sec θ + tan θ)­2
2(sec θ + tan θ)­3 ­2(sec θ tan θ + sec2θ)­3
2(sec θ + tan θ)­3(tan2 θ + sec θ tan θ) QUESTION 2 4 points Save Answer Write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x. y = tan
y = tan u; u = π ­ ; = sec2
y = tan u; u = π ­ ; = sec2
y = tan u; u = π ­ ; = sec2
y = tan u; u = π ­ ; = sec tan QUESTION 3 4 points Save Answer Write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x. y = cot(6x ­ 6)
y = cot u; u = 6x ­ 6; = ­ 6 csc2(6x ­ 6)
y = cot u; u = 6x ­ 6; = ­ 6 cot(6x ­ 6) csc(6x ­ 6)
y = 6u ­ 6; u = cot x; = ­ 6 cot x csc2 x
y = cot u; u = 6x ­ 6; = ­ csc2(6x ­ 6)
QUESTION 4 4 points Save Answer Find the derivative of the function. y = θ4e­2θ cos 6θ
6θ3e­2θ sin 6θ
θ3e­2θ(4 cos 6θ ­ 2θ cos 6θ ­ 6θ sin 6θ)
θ3e­2θ(4 cos 6θ ­ 2 cos 6θ + 6 cos 6θ)
56θ3e­2θ sin 6θ QUESTION 5 4 points Save Answer Find y". y = sin(3x2ex)
(x2 + 4x + 2)ex cos(3x2ex) + 3xex(x3 + 4x2 + 4x) cos(3x2ex)
6ex sin(3x2ex) ­ 6xex sin(3x2ex) 3(x2 + 4x + 2)ex cos(3x2ex) ­ 9xe2x(x3 + 4x2 + 4x) sin(3x2ex)
6xex cos (3x2ex) + 3x2ex cos (3x2ex) QUESTION 6 4 points Save Answer Find y". y = ­2x6(4x ­ 2)2
208x6 + 384x5 ­ 60x4 ­208x7 + 224x6 ­ 48x5 ­1792x6 + 1344x5 ­ 240x4
16x7 + 32x6 ­ 12x5 QUESTION 7 4 points Save Answer Find the derivative of the function. y = (1 + 6x)e­6x
36e­6x
6(1 + 6x)e­6x
6xe­6x
36xe­6x QUESTION 8 4 points Save Answer Use implicit differentiation to find dy/dx. x = sec(4y) cos(4y) cot(4y) sec(4y) tan(4y)
4 sec(4y) tan(4y)
cos(4y) cot(4y)
QUESTION 9 4 points Save Answer Find dy/dt. y = t7(t5 ­ 6)3
t6(t5 ­ 6)2(22t5 ­ 42)
t7(t5 ­ 6)2(22t4 ­ 42)
7t6(t5 ­ 6)2(15t5 ­ 6)
105t33(t5 ­ 6)2 QUESTION 10 Find dy/dt. 4
y = ­ sin e4 cos(t/9)
3 cos e4 cos(t/9) sin e3 cos(t/9) 4 points Save Answer sin e3 cos(t/9)
QUESTION 11 4 points Save Answer Find y". y = 2 cot ­4 csc ­ csc2 csc2 cot 4 csc2 cot QUESTION 12 4 points Save Answer Find y". y = tan(­9x ­ 5) sec2(­9x ­ 5) tan(­9x ­ 5)
sec2(­9x ­ 5) sec(­9x ­ 5) sec2(­9x ­ 5) tan(­9x ­ 5)
QUESTION 13 4 points Save Answer Use implicit differentiation to find dy/dx. x5 = cot y ­ ­ QUESTION 14 4 points Save Answer Use implicit differentiation to find dy/dx. cos xy + x3 = y3 QUESTION 15 4 points Save Answer Write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x. y = csc(cot x)
y = csc u; u = cot x; = ­ csc(cot x) cot(cot x)
y = cot u; u = csc x; = csc2(csc x) csc x cot x
y = csc u; u = cot x; = csc3 x cot x
y = csc u; u = cot x; = csc(cot x) cot(cot x) csc2 x
QUESTION 16 4 points Save Answer Find dy/dt. y = 5t(2t + 3)3
5(2t + 3)2
5(8t + 3)2 5(2t + 3)3(5t + 3)
5(2t + 3)2(8t + 3) QUESTION 17 4 points Save Answer Use implicit differentiation to find dy/dx. y cos = 7x + 7y QUESTION 18 4 points Save Answer Given y = f(u) and u = g(x), find dy/dx = f'(g(x))g'(x). y = sin u, u = cos x
cos x sin x
cos x sin x
sin(cos x) sin x
cos(cos x) sin x
QUESTION 19 4 points Save Answer Find the derivative of the function. 5 h(x) = 5 ­5 4 4
4 QUESTION 20 Given y = f(u) and u = g(x), find dy/dx = f'(g(x))g'(x). y = csc u, u = x6 + 9x
(6x5 + 9) cot2(x6 + 9x)
(6x5 + 9) csc x cot x ­(6x5 + 9) csc (x6 + 9x) cot (x6 + 9x)
csc (x6 + 9x) cot (x6 + 9x) 4 points Save Answer QUESTION 21 4 points Save Answer Find the derivative of the function. 3
y = (5x3 ­ 2x2 + 8x ­ 6)ex
3
(15x2 ­ 4x + 8)ex 3
(15x5 ­ 6x4 + 24x3 ­ 3x2 ­ 4x + 8)ex 3
(15x5 ­ 6x4 + 24x3 + 15x2 ­ 4x + 8)ex
3
(15x5 ­ 6x4 + 24x3 ­18x2)ex
QUESTION 22 4 points Save Answer Use implicit differentiation to find dy/dx. cos xy + x5 = y5 QUESTION 23 4 points Save Answer Write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x. y = e7x/2
y = eu; u = 7x/2; = e7x/2
y = eu; u = 7x/2; = e7x/2
y = eu; u = 7x/2; = xe7x/2
y = eu; u = 7x/2; = xe7x/2
QUESTION 24 4 points Save Answer Use implicit differentiation to find dy/dx. xy + x + y = x2y2 QUESTION 25 4 points Save Answer Given y = f(u) and u = g(x), find dy/dx = f'(g(x))g'(x). y = tan u, u = ­9x + 13
9 sec (­9x + 13) tan (­9x + 13)
sec2(­9x + 13)
9 sec2(­9x + 13)
sec2(­9x + 13) Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and Submit

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