# Important Derivatives Quiz 1

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

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

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

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

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

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

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

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

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

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

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

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

11. The derivative of a constant number is always

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

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

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

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

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

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

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

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

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

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

• The derivative of a constant number is always
• If $y=f(x)=\ln x$, then its $\frac{dy}{dx}$ will be _
• The gradient of the curve $y=2x^3 – 5x^2 – 3x$ at $x=0$ is
• Find $\frac{dy}{dx}$ where $y=e^0$?
• If $f(x) = \ln(a+b)$ then $f'(x)=$?
• $\frac{d}{dx} \, \sqrt{x}=$?
• If $y=ax^2+bx + c$ then $\frac{dy}{dx}=$?
• The derivative of $x^{-\frac{1}{2}}$ is
• $\frac{d}{dx}\, e^{2x}=$?
• If $y=\frac{x-1}{x+1}$ then $\frac{dy}{dx}=$?
• If $y=\frac{1-x^2}{1+x^2}$ then $\frac{dy}{dx}=$?
• If $y=e^{2x}(e^x+e^{-x})$ then $\frac{dy}{dx}=$?
• $\frac{d}{dx} e^{-x}=$?
• If $y=e^{x^2}$ then $\frac{dy}{dx}=$?
• If $f(x)=\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^2$ then $f'(x)=$?
• $\frac{d}{dx}\, \ln \left(x+\frac{1}{x}\right)=$?
• Derivative of $x^2$ with respect to $e^x$ is
• If $f(x)=(\sqrt{x}+1)(\sqrt{x}-1)$ then $f'(x)=$?
• If $y=(\sqrt[n]{x})^0$ then $\frac{dy}{dx}=$?
• The gradient of the curve $4x^3-7x^2+15$ at $x=0$ is

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