Direction:
1. Choose the appropriate answer to the derivative of trigonometric questions
2. After finished 10 questions, Click the button of "Check for All Questions"
3. For wrong answer, Click the button of "Show Answer" for seeing its correct answer
Question 1:Which one of the following is equal to the derivative of:
\[ y = arctan (x + 1) \]
1. \[ \frac{dy}{dx} = -\frac{1}{x^2 + 2x + 2} \]
2. \[ \frac{dy}{dx} = -\frac{1}{x^2 + 2x + 4} \]
3. \[ \frac{dy}{dx} = \frac{1}{x^2 + 2x + 4} \]
4. \[ \frac{dy}{dx} = \frac{1}{x^2 + 2x + 2} \]
Question 2:Which one of the following is equal to the derivative of:
\[ y = arcsin (x^2) \]
1. \[ \frac{dy}{dx} = -\frac{2x}{\sqrt{1 - x^2}} \]
2. \[ \frac{dy}{dx} = -\frac{1}{\sqrt{1 - x^2}} \]
3. \[ \frac{dy}{dx} = \frac{1}{\sqrt{1 - x^2}} \]
4. \[ \frac{dy}{dx} = \frac{2x}{\sqrt{1 - x^2}} \]
Question 3:Which one of the following is equal to the derivative of:
\[ y = (x)arcsin (2x) \]
1. \[ \frac{dy}{dx} = \frac{1}{\sqrt{1 - x^4}} + arcsin(2x) \]
2. \[ \frac{dy}{dx} = \frac{2x}{\sqrt{1 - x^4}} + arcsin(2x) \]
3. \[ \frac{dy}{dx} = -\frac{2x}{\sqrt{1 - x^4}} + arcsin(2x) \]
4. \[ \frac{dy}{dx} = -\frac{1}{\sqrt{1 - x^4}} - arcsin(2x) \]
Question 4:Which one of the following is equal to the derivative of:
\[ y = (arcsin(x))^2 \]
1. \[ \frac{dy}{dx} = -\frac{2arccos(x)}{\sqrt{1 - x^2}} \]
2. \[ \frac{dy}{dx} = \frac{2arccos(x)}{\sqrt{1 - x^2}} \]
3. \[ \frac{dy}{dx} = \frac{2arcsin(x)}{\sqrt{1 - x^2}} \]
4. \[ \frac{dy}{dx} = -\frac{2arcsin(x)}{\sqrt{1 - x^2}} \]
Question 5:Which one of the following is equal to the derivative of:
\[ y = arcsin \frac{c + r}{1 - cr}, c >0 \]
1. \[ \frac{dy}{dx} = -\frac{1}{\sqrt{1 + r^2}} \]
2. \[ \frac{dy}{dx} = -\frac{1}{\sqrt{1 - r^2}} \]
3. \[ \frac{dy}{dx} = \frac{1}{\sqrt{1 - r^2}} \]
4. \[ \frac{dy}{dx} = \frac{1}{\sqrt{1 + r^2}} \]
Question 6:Which one of the following is equal to the derivative of:
\[ θ = arcsin\sqrt{1 - r^2} \]
1. \[ \frac{dθ}{dr} = \frac{r}{|r|\sqrt{1 + r^2}} \]
2. \[ \frac{dθ}{dr} = \frac{r}{|r|\sqrt{1 - r^2}} \]
3. \[ \frac{dθ}{dr} = -\frac{r}{|r|\sqrt{1 + r^2}} \]
4. \[ \frac{dθ}{dr} = -\frac{r}{|r|\sqrt{1 - r^2}} \]
Question 7:Which one of the following is equal to the derivative of:
\[ f(x) = \sqrt{c - x^2} + (c)arcsin\frac{x}{c}, c>0 \]
1. \[ f^{'}(x) = \sqrt{\frac{c-x}{c+x}} \]
2. \[ f^{'}(x) = \sqrt{\frac{c+x}{c+x}} \]
3. \[ f^{'}(x) = \sqrt{\frac{c-x}{c-x}} \]
4. \[ f^{'}(x) = \sqrt{\frac{c+x}{c-x}} \]
Question 8:Which one of the following is equal to the value of:
\[ \int_{-1}^1 \frac{1}{1 + x^2}~dx \]
1. \[ Answer = \frac{π}{8} \]
2. \[ Answer = \frac{π}{6} \]
3. \[ Answer = \frac{π}{4} \]
4. \[ Answer = \frac{π}{2} \]
Question 9:Which one of the following is equal to the value of:
\[ \int_0^1 \frac{1}{\sqrt{4 - x^2}}~dx \]
1. \[ Answer = \frac{π}{2} \]
2. \[ Answer = \frac{π}{4} \]
3. \[ Answer = \frac{π}{6} \]
4. \[ Answer = \frac{π}{8} \]
Question 10:Which one of the following is equal to the value of:
\[ \int_0^1 \frac{1}{1 + x^2}~dx \]
1. \[ Answer = \frac{π}{2} \]
2. \[ Answer = \frac{π}{4} \]
3. \[ Answer = \frac{π}{6} \]
4. \[ Answer = \frac{π}{8} \]
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