L11 Continuity and Differentiability

रो कर मुस्कुराने का मजा ही कुछ और होता है,
जिंदगी में कुछ खो कर पाने का मजा ही कुछ और होता है,
ज़िन्दगी में हार और जीत तो लगी रहती है,
लेकिन हार के जीतने का मजा ही कुछ और होता है।

Lecture - 11 Chapter 5 Continuity and Differentiability

In this lecture, I am discussing miscellaneous questions of differentiation which are based on chain rule, logarithmic differentiation, derivative of implicit functions, derivative of parametric functions etc. All these questions are from NCERT Miscellaneous Exercise of Chapter 5 Class 12 Maths Continuity and Differentiability.

Questions discussed in this lecture:


Differentiate w.r.t. x the function in Exercises 1 to 11.

Question 1. (3x^2 – 9x + 5)^9

Question 2. \sin^3{x} + \cos^6{x}

Question 3. (5x)^{3 \cos 2x}

Question 4. \sin^{-1}(x\sqrt{x}), 0 \le x \le 1

Question 5. \frac{\cos^{-1}\frac{x}{2}}{\sqrt{2x+7}}, -2<x<2

Question 6. \cot^{-1} \left[ \frac{\sqrt{1 + \sin x} + \sqrt{1 – \sin x}}{\sqrt{1 + \sin x} – \sqrt{1 – \sin x}} \right], 0<x<\frac{\pi}{2}

Question 7. (\log x)^{\log x}, x>1

Question 8. \cos(a \cos x + b \sin x) , for some constant a and b.

Question 9. (\sin x – \cos x)^{(\sin x – \cos x)}, \frac{\pi}{4}<x<\frac{3\pi}{4}

Question 10. x^x + x^a + a^x + a^a

Question 11. x^{x^2 – 3} + (x – 3)^{x^2}