Derivative MCQs (1)

1. What is derivative of $\sqrt{1-x}$?

$\displaystyle \frac{1}{2\sqrt{1-x}}$
$\displaystyle \frac{-1}{2\sqrt{1-x}}$
$\displaystyle \sqrt{1}$
None of above

2. What is value of $\displaystyle \frac{dy}{dx}$ when $y=\displaystyle \frac{1}{x}$ at $x=2$?

$1$
$-4$
$\displaystyle \frac{-1}{4}$
$\displaystyle \frac{-1}{2}$

3. What is the value of $\displaystyle \frac{d}{dx}(2^x)$ at $x=1$ ?

$-2\ln(2)$
$2\ln(2)$
$\ln(2)$
None of above

4. What is the value of $\displaystyle \frac{d}{dx}(\sin⁡ x .\tan⁡ x)$?

$\sin⁡ x + \tan⁡ x$
$\sin⁡ x + \tan⁡ x \sec⁡ x$
$\sin⁡ x + \tan⁡ x \sec2⁡x$
None of above

5. Find the $\displaystyle \frac{d}{dx}(e^{(x^2+x)})$ at $x=1$?

$3e^{3}$
$2e^{2}$
$3e^{2}$
None of above

6. What is the value of $\displaystyle \frac{d}{dx}(\cos^{2}⁡ x .\tan⁡ x)$ at $x = 0$?

$-1$
$0$
$2$
$1$

7. Derivative of $\cos^{3}(x+x^2)$?

$-3\sin^{2}(1+2x)$
$-3\cos^{2}(1+2x)\sin(x+x^2)$
$-3\cos^{2}(x+x^2).\sin(x+x^2)(1+x^2)$
$-3\cos^{2}(x+x^2).\sin(x+x^2)(1+2x)$

8. Derivative of $y=\sin^{-1} (x^2)$?

$\displaystyle \frac{2x}{\sqrt{1-x^2}}$
$\displaystyle \frac{1}{\sqrt{1-x^2}}$
$\displaystyle \frac{-1}{\sqrt{1-x^2}}$
None of above

9. What is the value of $\displaystyle \frac{d}{dx}(\cos(x))$ at $x=60^{0}$?

$\displaystyle \frac{-\sqrt{3}}{2}$
$\displaystyle \frac{-1}{2}$
$\displaystyle \frac{1}{2}$
None of above

10. What is value of $\displaystyle \frac{dy}{dx}$ where $y=e^{3x+7}$ ?

$e^{3x+7}$
$7e^{3x+7}$
$e^{3}$
$3e^{3x+7}$