Calculus Quiz

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QUESTION 1

· Find the derivative of the function. y = θ4e-2θ cos 6θ

		θ3e-2θ(4 cos 6θ - 2 cos 6θ + 6 cos 6θ)
		θ3e-2θ(4 cos 6θ - 2θ cos 6θ - 6θ sin 6θ)
		-6θ3e-2θ sin 6θ
		-56θ3e-2θ sin 6θ

4 points

QUESTION 2

· 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
		- cos(cos x) sin x
		sin(cos x) sin x

4 points

QUESTION 3

· Find dy/dt. y = t7(t5 - 6)3

		t6(t5 - 6)2(22t5 - 42)
		105t33(t5 - 6)2
		7t6(t5 - 6)2(15t5 - 6)
		t7(t5 - 6)2(22t4 - 42)

4 points

QUESTION 4

· Find y". y = 2 cot $C:\Users\john.morris\Desktop\f1q16g1.jpg$

		- $C:\Users\john.morris\Desktop\f1q16g8.jpg$ csc2 $C:\Users\john.morris\Desktop\f1q16g1.jpg$
		4 csc2 $C:\Users\john.morris\Desktop\f1q16g1.jpg$ cot $C:\Users\john.morris\Desktop\f1q16g1.jpg$
		-4 csc $C:\Users\john.morris\Desktop\f1q16g1.jpg$
		$C:\Users\john.morris\Desktop\f1q16g5.jpg$ csc2 $C:\Users\john.morris\Desktop\f1q16g1.jpg$ cot $C:\Users\john.morris\Desktop\f1q16g1.jpg$

4 points

QUESTION 5

· Find the derivative of the function. h(x) = $C:\Users\john.morris\Desktop\f1q8g1.jpg$ 5

		-5 $C:\Users\john.morris\Desktop\f1q8g4.jpg$ 4
		5 $C:\Users\john.morris\Desktop\f1q8g1.jpg$ 4
	$C:\Users\john.morris\Desktop\f1q8g2.jpg$	$C:\Users\john.morris\Desktop\f1q8g1.jpg$ 4
	$C:\Users\john.morris\Desktop\f1q8g5.jpg$

4 points

QUESTION 6

· Use implicit differentiation to find dy/dx. y cos $C:\Users\john.morris\Desktop\f1q24g1.jpg$ = 7x + 7y

		$C:\Users\john.morris\Desktop\f1q24g4.jpg$
		$C:\Users\john.morris\Desktop\f1q24g2.jpg$
		$C:\Users\john.morris\Desktop\f1q24g3.jpg$
		$C:\Users\john.morris\Desktop\f1q24g5.jpg$

4 points

QUESTION 7

· Use implicit differentiation to find dy/dx. cos xy + x5 = y5

		$C:\Users\john.morris\Desktop\f1q23g1.jpg$
		$C:\Users\john.morris\Desktop\f1q23g4.jpg$
		$C:\Users\john.morris\Desktop\f1q23g2.jpg$
		$C:\Users\john.morris\Desktop\f1q23g3.jpg$

4 points

QUESTION 8

· 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; $C:\Users\john.morris\Desktop\f1q6g2.jpg$ = - 6 csc2(6x - 6)
		y = 6u - 6; u = cot x; $C:\Users\john.morris\Desktop\f1q6g2.jpg$ = - 6 cot x csc2 x
		y = cot u; u = 6x - 6; $C:\Users\john.morris\Desktop\f1q6g2.jpg$ = - 6 cot(6x - 6) csc(6x - 6)
		y = cot u; u = 6x - 6; $C:\Users\john.morris\Desktop\f1q6g2.jpg$ = - csc2(6x - 6)

4 points

QUESTION 9

· Find dy/dt. y = 5t(2t + 3)3

		5(2t + 3)3(5t + 3)
		5(2t + 3)2(8t + 3)
		5(2t + 3)2
		5(8t + 3)2

4 points

QUESTION 10

· Use implicit differentiation to find dy/dx. x5 = cot y

		$C:\Users\john.morris\Desktop\f1q21g1.jpg$
		$C:\Users\john.morris\Desktop\f1q21g2.jpg$
		- $C:\Users\john.morris\Desktop\f1q21g2.jpg$
		- $C:\Users\john.morris\Desktop\f1q21g4.jpg$

4 points

QUESTION 11

· Use implicit differentiation to find dy/dx. xy + x + y = x2y2

		$C:\Users\john.morris\Desktop\f1q20g1.jpg$
		$C:\Users\john.morris\Desktop\f1q20g4.jpg$
		$C:\Users\john.morris\Desktop\f1q20g2.jpg$
		$C:\Users\john.morris\Desktop\f1q20g3.jpg$

4 points

QUESTION 12

· 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)
		-9 sec2(-9x + 13)
		- sec2(-9x + 13)
		sec2(-9x + 13)

4 points

QUESTION 13

· Find y". y = $C:\Users\john.morris\Desktop\f1q17g1.jpg$ tan(-9x - 5)

		$C:\Users\john.morris\Desktop\f1q17g2.jpg$ sec2(-9x - 5) tan(-9x - 5)
		$C:\Users\john.morris\Desktop\f1q17g2.jpg$ sec(-9x - 5)
		$C:\Users\john.morris\Desktop\f1q17g4.jpg$ sec2(-9x - 5) tan(-9x - 5)
		- $C:\Users\john.morris\Desktop\f1q17g5.jpg$ sec2(-9x - 5)

4 points

QUESTION 14

· Write the function in the form y = f(u) and u = g(x). Then find dy/dx as a function of x. y = tan $C:\Users\john.morris\Desktop\f1q5g1.jpg$

		y = tan u; u = π - $C:\Users\john.morris\Desktop\f1q5g13.jpg$ ; $C:\Users\john.morris\Desktop\f1q5g14.jpg$ = $C:\Users\john.morris\Desktop\f1q5g15.jpg$ sec2 $C:\Users\john.morris\Desktop\f1q5g1.jpg$
		y = tan u; u = π - $C:\Users\john.morris\Desktop\f1q5g13.jpg$ ; $C:\Users\john.morris\Desktop\f1q5g14.jpg$ = sec2 $C:\Users\john.morris\Desktop\f1q5g1.jpg$
		y = tan u; u = π - $C:\Users\john.morris\Desktop\f1q5g13.jpg$ ; $C:\Users\john.morris\Desktop\f1q5g14.jpg$ = sec2 $C:\Users\john.morris\Desktop\f1q5g15.jpg$
		y = tan u; u = π - $C:\Users\john.morris\Desktop\f1q5g13.jpg$ ; $C:\Users\john.morris\Desktop\f1q5g14.jpg$ = $C:\Users\john.morris\Desktop\f1q5g15.jpg$ sec $C:\Users\john.morris\Desktop\f1q5g1.jpg$ tan $C:\Users\john.morris\Desktop\f1q5g1.jpg$

4 points

QUESTION 15

· Find the derivative of the function. y = (1 + 6x)e-6x

		-6(1 + 6x)e-6x
		-36xe-6x
		6xe-6x
		-36e-6x

4 points

QUESTION 16

· 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; $C:\Users\john.morris\Desktop\f1q7g3.jpg$ = $C:\Users\john.morris\Desktop\f1q7g4.jpg$ e7x/2
		y = eu; u = 7x/2; $C:\Users\john.morris\Desktop\f1q7g3.jpg$ = $C:\Users\john.morris\Desktop\f1q7g4.jpg$ xe7x/2
		y = eu; u = 7x/2; $C:\Users\john.morris\Desktop\f1q7g3.jpg$ = $C:\Users\john.morris\Desktop\f1q7g4.jpg$ xe7x/2
		y = eu; u = 7x/2; $C:\Users\john.morris\Desktop\f1q7g3.jpg$ = $C:\Users\john.morris\Desktop\f1q7g4.jpg$ e7x/2

4 points

QUESTION 17

· Find dy/dt. y = $C:\Users\john.morris\Desktop\f1q15g1.jpg$ 4

		- $C:\Users\john.morris\Desktop\f1q15g8.jpg$ sin $C:\Users\john.morris\Desktop\f1q15g9.jpg$ e4 cos(t/9)
		$C:\Users\john.morris\Desktop\f1q15g8.jpg$ sin $C:\Users\john.morris\Desktop\f1q15g9.jpg$ e3 cos(t/9)
		$C:\Users\john.morris\Desktop\f1q15g8.jpg$ cos $C:\Users\john.morris\Desktop\f1q15g9.jpg$ e4 cos(t/9)
		- $C:\Users\john.morris\Desktop\f1q15g8.jpg$ $C:\Users\john.morris\Desktop\f1q15g5.jpg$ 3

4 points

QUESTION 18

· Find y". y = -2x6(4x - 2)2

		-208x6 + 384x5 - 60x4
		-16x7 + 32x6 - 12x5
		-208x7 + 224x6 - 48x5
		-1792x6 + 1344x5 - 240x4

4 points

QUESTION 19

· Given y = f(u) and u = g(x), find dy/dx = f'(g(x))g'(x). y = csc u, u = x6 + 9x

		- csc (x6 + 9x) cot (x6 + 9x)
		-(6x5 + 9) csc (x6 + 9x) cot (x6 + 9x)
		-(6x5 + 9) csc x cot x
		-(6x5 + 9) cot2(x6 + 9x)

4 points

QUESTION 20

· 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; $C:\Users\john.morris\Desktop\f1q4g4.jpg$ = csc3 x cot x
		y = cot u; u = csc x; $C:\Users\john.morris\Desktop\f1q4g4.jpg$ = csc2(csc x) csc x cot x
		y = csc u; u = cot x; $C:\Users\john.morris\Desktop\f1q4g4.jpg$ = csc(cot x) cot(cot x) csc2 x
		y = csc u; u = cot x; $C:\Users\john.morris\Desktop\f1q4g4.jpg$ = - csc(cot x) cot(cot x)

4 points

QUESTION 21

· Find the derivative of the function. r = (sec θ + tan θ)-2

		$C:\Users\john.morris\Desktop\f1q9g1.jpg$
		-2(sec θ + tan θ)-3(tan2 θ + sec θ tan θ)
		-2(sec θ tan θ + sec2θ)-3
		-2(sec θ + tan θ)-3

4 points

QUESTION 22

· Use implicit differentiation to find dy/dx. x = sec(4y)

		4 sec(4y) tan(4y)
		$C:\Users\john.morris\Desktop\f1q25g2.jpg$ cos(4y) cot(4y)
		$C:\Users\john.morris\Desktop\f1q25g2.jpg$ sec(4y) tan(4y)
		cos(4y) cot(4y)

4 points

QUESTION 23

· Find the derivative of the function. y = (5x3 - 2x2 + 8x - 6)ex3

		(15x5 - 6x4 + 24x3 + 15x2 - 4x + 8)ex3
		(15x5 - 6x4 + 24x3 -18x2)ex3
		(15x5 - 6x4 + 24x3 - 3x2 - 4x + 8)ex3
		(15x2 - 4x + 8)ex3

4 points

QUESTION 24

· Find y". y = sin(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)
		(x2 + 4x + 2)ex cos(3x2ex) + 3xex(x3 + 4x2 + 4x) cos(3x2ex)

4 points

QUESTION 25

· Use implicit differentiation to find dy/dx. cos xy + x3 = y3

		$C:\Users\john.morris\Desktop\f1q22g1.jpg$
		$C:\Users\john.morris\Desktop\f1q22g3.jpg$
		$C:\Users\john.morris\Desktop\f1q22g2.jpg$
		$C:\Users\john.morris\Desktop\f1q22g4.jpg$