Lesson Example Discussion Quiz: Class Homework |
Quiz At Home |
Title: Differentiation |
Grade: 10-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: at Home
| Problem Id | Problem | Options |
|---|---|---|
1 |
Find the derivative of the function \$f(x) = ln(5x^2 + 3x)\$. |
A) \$ (15x - 3) / (5x^2 + 3x) \$ B) \$ (10x + 3) / (5x^2 + 3x) \$ C) \$ (10x + 3) * (5x^2 + 3x) \$ D) \$ (5x^2 + 3x) / (10x + 3)\$ |
2 |
Find the derivative of the function \$f(x) = sin(x^2) / x\$. |
A) \$ (2x^2cos(x^2) + sin(x^2)) / x^2 \$ B) \$ (2x^2sin(x^2) - cos(x^2)) / x^2 \$ C) \$ (2x^2cos(x^2) - sin(x^2)) / x^2 \$ D) \$ (2x^2sin(x^2) + cos(x^2)) / x^2 \$ |
3 |
Find the derivative of the function \$f(x) = (3x^2 + 2x - 1)^(4x+1)\$. |
A) \$ (2ln(3x^2 + 2x - 1) + ((6x - 3)(4x + 1))/(3x^2 + 2x - 1)) + (3x^2 + 2x - 1)^(4x + 1)\$ B) \$ (3ln(3x^2 + 2x - 1) + ((6x + 3)(4x + 1))/(3x^2 + 2x - 1))((3x^2 + 2x - 1)^(4x + 3))\$ C) \$ ((2ln(3x^2 + 2x - 1))/(3x^2 + 2x - 1))((3x^2 + 2x - 1)^(4x + 1))\$ D) \$ (4ln(3x^2 + 2x - 1) + ((6x + 2)(4x + 1))/(3x^2 + 2x - 1))((3x^2 + 2x - 1)^(4x + 1))\$ |
4 |
Find the derivative of the function \$f(x) = sqrt((3x^2 + 2)/(x^3 + 1))\$. |
A) \$ (-3x^4 - 6x^2 + 6x)/(2(3x^2 + 2)^(1/2) (x^3 + 1)^(3/2)) \$ B) \$ (-3x^4 - 6x^2 + 6x)/(2 (x^3 + 1)^3) \$ C) \$ (-3x^4 - 6x^2 + 6x)/((3x^2 + 2)^(1/2) (x^3 + 1)^(1/2)) \$ D) \$ (-3x^4 - 6x^2 + 6x)/((3x^2 + 2)^(-1/2) (x^3 + 1)^(3/2)) \$ |
5 |
Find the derivative of the function \$f(x) = e^(2x) * cos(3x)\$. |
A) \$ 2e^(2x)cos(3x) - 3e^(2x) * sin(3x) \$ B) \$ e^(2x)/2cos(3x) - e^(2x) * sin(3x)/3 \$ C) \$ 2e^(2x)sin(3x) - 3e^(2x) * cos(3x) \$ D) \$ 2e^(2x) cos(3x)/3 + 3e^(2x)/2 * sin(3x) \$ |
6 |
Find the derivative of the function \$f(x) = (x^2 + 1)^(x^2)\$. |
A) \$ ( 2xln(x^2 + 1) + (2x^3)/(x^2 + 1) )(x^2 + 1)^(x^2) \$ B) \$ 2x^3(x^2 - 1)^(x^2 + 1) \$ C) \$ ( ln(x^2 + 1) + (3x^2)/(x^3 + 1) )(x^2 + 1)^(x^2) \$ D) \$ ( ln(x^2 - 1) - (2x^2)/(x^3 - 1) )(x^2 - 1)^(x^2) \$ |
7 |
Find the derivative of the function \$f(x) = x^2 * ln(x^3 + 1)\$. |
A) \$ 2xln(x^3 + 1) + (3x^4) / (x^3 + 1) \$ B) \$ 2xln(x^3 + 1) + (x^3) / (x^3 + 1) \$ C) \$ (2x) / ln(x^3 + 1) + (3x^2) / (x^3 + 1) \$ D) \$ ln(x^3 + 1) + (3x^4) / (x^3 + 1) \$ |
8 |
Find the derivative of the function \$f(x) = sqrt(1 + cos^2(x))\$. |
A) \$ (cos(x) * sin(x)) / sqrt(1 + cos^2(x)) \$ B) \$ (- sin(2x)) /(2 sqrt(1 + cos^2(x))) \$ C) \$ - 2cos(x) * sin(x) * sqrt(1 + cos^2(x)) \$ D) \$ - cos(x) * sin(x) / 2sqrt(1 + cos^2(x)) \$ |
9 |
Find the derivative of the function \$f(x) = sqrt(x) + 2x^3 - e^x\$. |
A) \$ 1/(\sqrt x) + 6x^2 - e^x \$ B) \$ 2/( \sqrt x) + 6x^2 - e^x \$ C) \$ 1/(2 \sqrt x) + 6x^2 - e^x \$ D) \$ 1/(2 \sqrt x) - 6x^2 + e^x \$ |
10 |
Find the derivative of the function \$f(x) = e^(2x) + 3ln(x) - x^2\$. |
A) \$ e^(2x)/2 + 3/x - 2x \$ B) \$ e^(2x) + 3/x - 2x \$ C) \$ 2e^(2x) + x/3 - 2x \$ D) \$ 2e^(2x) + 3/x - 2x \$ |
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