“ख्वाहिशों” से नही गिरते हैं, “फूल” झोली में,

कर्म की साख़ को हिलाना होगा,

कुछ नही होगा कोसने से किस्मत को,

अपने हिस्से का दीया ख़ुद ही जलाना होगा।

# Lecture - 10 Chapter 5 Continuity and Differentiability

In this lecture, I am discussing about second order differentiation, which is also known as double derivatives.Also, I am discussing questions from NCERT Exercise 5.7 which are based on second order derivatives.

**Questions discussed in this lecture:**

NCERT EXERCISE 5.7 (Second Order Derivatives) |

Find the second order derivatives of the functions given in Exercises 1 to 10.

Question 1. x^2 + 3x + 2

Question 2. x^20

Question 3. x. \cos x

Question 4. \log x

Question 5. x^3 \log x

Question 6. e^x \sin 5x

Question 7. e^{6x} \cos 3x

Question 8. \tan^{-1}x

Question 9. \log(\log x)

Question 10. \sin(\log x)

Question 11. If y = 5 \cos x – 3 \sin x , prove that \frac{d^2{y}}{dx^2} + y = 0 .

Question 12. If y = \cos^{-1}x , Find \frac{d^2{y}}{dx^2} in terms of y alone.

Question 13. If y = 3 \cos(\log x) + 4\sin(\log x) , show that x^2{y_2} + x{y_1} + y = 0 .

Question 14. If y = Ae^{mx} + Be^{nx}, show that \frac{d^2{y}}{dx^2} – (m + n)\frac{dy}{dx} + mny = 0 .

Question 15. If y = 500e^{7x} + 600e^{-7x}, show that \frac{d^2{y}}{dx^2} = 49y .

Question 16. If e^y(x+1) = 1 , show that \frac{d^2{y}}{dx^2} = \left( \frac{dy}{dx} \right)^2.

Question 17. If y = (\tan^{-1}x)^2 , show that (x^2 + 1)^2 y_2 + 2x (x^2 + 1) y_1 = 2 .