Category: Calculus

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

18. The derivative of a constant number is always

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

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