# Lecture 10 Class 11 Limits and Derivatives

If you don’t design your own life plan, chances are you’ll fall into someone else’s plan. And guess what they have planned for you? Not much. – Jim Rohn

# Lecture - 10 Chapter 13 Limits and Derivatives

 MISCELLANEOUS EXERCISE

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Question 2. $$(x+a)$$

Question 3. $$(px+q) \left ( \frac{r}{x} + s \right )$$

Question 5. $$\frac{ax+b}{cx+d}$$

Question 6. $$\frac{1+\frac{1}{x}}{1-\frac{1}{x}}$$

Question 7. $$\frac{1}{ax^2+bx+c}$$

Question 8. $$\frac{ax+b}{px^2+qx+r}$$

Question 9. $$\frac{px^2+qx+r}{ax+b}$$

Question 10. $$\frac{a}{x^4}-\frac{b}{x^2}+\cos x$$

Question 11. $$4 \sqrt{x}-2$$

Question 15. $$\cosec x \cot x$$

##### Clip - 1

Question 16. $$\frac{\cos x}{1+ \sin x}$$

Question 17. $$\frac{\sin x + \cos x}{\sin x – \cos x}$$

Question 18. $$\frac{\sec x – 1}{\sec x + 1}$$

Question 20. $$\frac{a+b \sin x}{c + d \cos x}$$

Question 22. $$x^4(5 \sin x – 3 \cos x)$$

Question 23.  $$(x^2+1) \cos x$$

Question 24. $$(ax^2+ \sin x)(p + q \cos x)$$

Question 25. $$(x + \cos x)(x – \tan x)$$

Question 26. $$\frac{4x+5 \sin x}{3x+8 \cos x}$$

Question 27. $$\frac{x^2 \cos \left ( \frac{\pi}{4} \right ) }{\sin x}$$

Question 28. $$\frac{x}{1+ \tan x}$$

Question 29. $$(x + \sec x)(x – \tan x)$$