# Tag: Derivatives

## Derivatives

This is the Multiple Choice Questions Test in Differential Calculus (Limits and Derivatives) a topic in Business Mathematics.

MCQs about Derivatives for the preparation of Business Mathematics and Exams related to ICMAP, CA, Commerce, and Business Studies.

1. If $y=e^{x^2}$ then $\frac{dy}{dx}=$?

2. The derivative of a constant number is always

3. $\frac{d}{dx} \, \sqrt{x}=$?

4. If $y=(\sqrt[n]{x})^0$ then $\frac{dy}{dx}=$?

5. If $y=ax^2+bx + c$ then $\frac{dy}{dx}=$?

6. If $f(x) = \ln(a+b)$ then $f'(x)=$?

7. The gradient of the curve $4x^3-7x^2+15$ at $x=0$ is

8. The derivative of $x^{-\frac{1}{2}}$ is

9. If $y=e^{2x}(e^x+e^{-x})$ then $\frac{dy}{dx}=$?

10. $\frac{d}{dx} e^{-x}=$?

11. If $y=\frac{x-1}{x+1}$ then $\frac{dy}{dx}=$?

12. $\frac{d}{dx}\, \ln \left(x+\frac{1}{x}\right)=$?

13. $\frac{d}{dx}\, e^{2x}=$?

14. The gradient of the curve $y=2x^3 – 5x^2 – 3x$ at $x=0$ is

15. If $f(x)=(\sqrt{x}+1)(\sqrt{x}-1)$ then $f'(x)=$?

16. If $y=f(x)=\ln x$, the its $\frac{dy}{dx}$ will be ___________

17. Find $\frac{dy}{dx}$ where $y=e^0$?

18. If $y=\frac{1-x^2}{1+x^2}$ then $\frac{dy}{dx}=$?

19. Derivative of $x^2$ with respect to $e^x$ is

20. If $f(x)=\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^2$ then $f'(x)=$?

The questions are designed to help and gain deep understanding of the concept related to derivatives.