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Lesson Example Discussion Quiz: Class Homework

Quiz At Home

Title: Differentiation

Grade: 1400-a Lesson: S2-L5

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: in Class

Problem Id	Problem	Options
1	Find the derivative of the function: \$f(x) = (x^2 -3x + 2) / x\$.	A) \$f(x) = 1 + (3 / x^2)\$ B) \$f(x) = 1 - (2 / x^2)\$ C) \$f(x) = 1 - (2 / x^3)\$ D) \$f(x) = 1 - (5 / x^2)\$
2	Find the derivative of function \$g(x) = In(x^2 + 1)\$.	A) \$g(x) = (2x) / (x^2 + 5)\$ B) \$g(x) = (2x) / (x^2 + 3)\$ C) \$g(x) = (2x) / (x^2 + 1)\$ D) \$g(x) = (2x) / (x^3 - 1)\$
3	Determine where, if anywhere, the function \$f(x) = x^3 + 9x^2 - 48x + 2\$ is not changing.	A) x = - 8 and x = - 2 B) x = 8 and x = 2 C) x = 8 and x = - 2 D) x = - 8 and x = 2
4	Find the derivative of the function \$h(x) = e^2x sin(x)\$.	A) \$h(x) = 2e^2x sin(x) + e^2x cos(x)\$. B) \$h(x) = 2e^2x sin(x) - e^3x cos(y)\$. C) \$h(x) = 3e^3x sin(x) + e^2x cos(x)\$. D) \$h(x) = 2e^3x sin(x) + e^3x cos(x)\$.
5	Find the derivative of the function: \$f(x) = \sqrt(1 - x^2) \$.	A) \$f(x) = -x / (\sqrt(1 - x^2))\$ B) \$f(x) = (2x) / (\sqrt(1 + x^2))\$ C) \$f(x) = -x / (\sqrt(3 - x^3))\$ D) \$f(x) = -(2x) / (\sqrt(1 + x^2))\$
6	For the equation \$ sin(xy) + e^xy = x^2 + y^2 \$, find \$ dy/dx \$.	A) \$ (2x - ycos(xy) - e^(xy)y)/(xcos(xy) + e^(xy)x - 2y) \$ B) \$ (4x − y(cos(xy) + e^xy))/(x(cos(xy) + e^xy) − 2y) \$ C) \$ (2x − y(cos(xy) + e^xy))/(2x(cos(xy) + e^xy) − 2y) \$ D) \$ (4x − y(cos(xy) + e^xy))/(x(cos(xy) + e^xy) − 4y) \$
7	Differentiate \$ y = (x^2 + 1)^sinx \$.	A) \$ (x^2 + 1)^sin(x) ( (2x sin(x))/(x^2 + 1) + ln(x^2 + 1) cos(x)) \$ B) \$ (2x^2 + 1)^sinx ((sinx (2x))/(x^2 + 1) + ln(x^2+1) cosx) \$ C) \$ (x^2 + 1)^sinx ((sinx (2x))/(x^2 + 1) + 2ln(x^2+1) cosx) \$ D) \$ (4x^2 + 1)^sinx ((sinx (4x))/(x^2 + 1) + 2ln(x^2+1) cosx) \$
8	For the equation \$ x^3 + y^3 = 6xy \$, find \$ dy/dx \$.	A) \$ (3y − x^2)/(y^2 − 2x) \$ B) \$ (2y − x^2)/(y^2 − 2x) \$ C) \$ (4y − x^2)/(y^2 − 2x) \$ D) \$ (y − x^2)/(y^2 − x) \$
9	Find the derivative of \$ y= (sin(x))^cos(x)/2 \$.	A) \$ (1/4)sin^(cos(x))(x) (sin(x) ln(sin(x)) + 2cot(x)cos(x)) \$ B) \$ ((sin(x))^cos(x)/(cos(x))^sin(x)) (cos^2(x) cot(x) + sin^3(x) tan(x)) \$ C) \$ (1/2)sin^(cos(x))(x) (-sin(x) ln(sin(x)) + 2cot(x)cos(x)) \$ D) \$ ((sin(x))^cos(x)/(cos(x))^sin(x)) (cos^4(x) cot(x) + sin^4(x) tan(x)) \$
10	A 15-foot ladder is resting against a wall. The bottom is initially 10 ft away and pushed towards the wall at \$ 1/4 (ft)/sec \$. How fast is the top moving after 12 sec?	A) \$ 1/(4\sqrt(176)) (ft)/sec \$ B) \$ 7/(2\sqrt(176)) (ft)/sec \$ C) \$ 7/(4\sqrt(236)) (ft)/sec \$ D) \$ 7/(4\sqrt(176)) (ft)/sec \$

Problem Id

Problem

Options

Find the derivative of the function: \$f(x) = (x^2 -3x + 2) / x\$.

A) \$f(x) = 1 + (3 / x^2)\$

B) \$f(x) = 1 - (2 / x^2)\$

C) \$f(x) = 1 - (2 / x^3)\$

D) \$f(x) = 1 - (5 / x^2)\$

Find the derivative of function \$g(x) = In(x^2 + 1)\$.

A) \$g(x) = (2x) / (x^2 + 5)\$

B) \$g(x) = (2x) / (x^2 + 3)\$

C) \$g(x) = (2x) / (x^2 + 1)\$

D) \$g(x) = (2x) / (x^3 - 1)\$

Determine where, if anywhere, the function \$f(x) = x^3 + 9x^2 - 48x + 2\$ is not changing.

A) x = - 8 and x = - 2

B) x = 8 and x = 2

C) x = 8 and x = - 2

D) x = - 8 and x = 2

Find the derivative of the function \$h(x) = e^2x sin(x)\$.

A) \$h(x) = 2e^2x sin(x) + e^2x cos(x)\$.

B) \$h(x) = 2e^2x sin(x) - e^3x cos(y)\$.

C) \$h(x) = 3e^3x sin(x) + e^2x cos(x)\$.

D) \$h(x) = 2e^3x sin(x) + e^3x cos(x)\$.

Find the derivative of the function: \$f(x) = \sqrt(1 - x^2) \$.

A) \$f(x) = -x / (\sqrt(1 - x^2))\$

B) \$f(x) = (2x) / (\sqrt(1 + x^2))\$

C) \$f(x) = -x / (\sqrt(3 - x^3))\$

D) \$f(x) = -(2x) / (\sqrt(1 + x^2))\$

For the equation \$ sin(xy) + e^xy = x^2 + y^2 \$, find \$ dy/dx \$.

A) \$ (2x - ycos(xy) - e^(xy)y)/(xcos(xy) + e^(xy)x - 2y) \$

B) \$ (4x − y(cos(xy) + e^xy))/(x(cos(xy) + e^xy) − 2y) \$

C) \$ (2x − y(cos(xy) + e^xy))/(2x(cos(xy) + e^xy) − 2y) \$

D) \$ (4x − y(cos(xy) + e^xy))/(x(cos(xy) + e^xy) − 4y) \$

Differentiate \$ y = (x^2 + 1)^sinx \$.

A) \$ (x^2 + 1)^sin(x) ( (2x sin(x))/(x^2 + 1) + ln(x^2 + 1) cos(x)) \$

B) \$ (2x^2 + 1)^sinx ((sinx (2x))/(x^2 + 1) + ln(x^2+1) cosx) \$

C) \$ (x^2 + 1)^sinx ((sinx (2x))/(x^2 + 1) + 2ln(x^2+1) cosx) \$

D) \$ (4x^2 + 1)^sinx ((sinx (4x))/(x^2 + 1) + 2ln(x^2+1) cosx) \$

For the equation \$ x^3 + y^3 = 6xy \$, find \$ dy/dx \$.

A) \$ (3y − x^2)/(y^2 − 2x) \$

B) \$ (2y − x^2)/(y^2 − 2x) \$

C) \$ (4y − x^2)/(y^2 − 2x) \$

D) \$ (y − x^2)/(y^2 − x) \$

Find the derivative of \$ y= (sin(x))^cos(x)/2 \$.

A) \$ (1/4)sin^(cos(x))(x) (sin(x) ln(sin(x)) + 2cot(x)cos(x)) \$

B) \$ ((sin(x))^cos(x)/(cos(x))^sin(x)) (cos^2(x) cot(x) + sin^3(x) tan(x)) \$

C) \$ (1/2)sin^(cos(x))(x) (-sin(x) ln(sin(x)) + 2cot(x)cos(x)) \$

D) \$ ((sin(x))^cos(x)/(cos(x))^sin(x)) (cos^4(x) cot(x) + sin^4(x) tan(x)) \$

A 15-foot ladder is resting against a wall. The bottom is initially 10 ft away and pushed towards the wall at \$ 1/4 (ft)/sec \$. How fast is the top moving after 12 sec?

A) \$ 1/(4\sqrt(176)) (ft)/sec \$

B) \$ 7/(2\sqrt(176)) (ft)/sec \$

C) \$ 7/(4\sqrt(236)) (ft)/sec \$

D) \$ 7/(4\sqrt(176)) (ft)/sec \$