जीत निश्चित हो तो कायर भी लड़ सकते हैं, बहादुर वे कहलाते हैं, जो हार निश्चित हो, फिर भी मैदान नहीं छोड़ते…

In this lecture, I am discussing few questions based on derivatives of logarithmic and exponential functions. Also, when and how to use Logarithms in Differentiation?

Questions discussed in this lecture:

NCERT EXERCISE 5.4

Differentiate the following w.r.t. x:

Question 1. \( \frac{e^x}{\sin x}\)
Question 2. \( e^{\sin^{-1}x} \)
Question 3. \( e^{x^3} \)
Question 4. \( \sin(\tan^{-1} e^{-x}) \)
Question 5. \( \log (\cos e^x) \)
Question 6. \( e^x + e^{x^2} +…+ e^{x^5} \)
Question 7. \( \sqrt{e^{\sqrt{x}}}, x>0 \)
Question 8. \( \log(\log x), x>1 \)
Question 9. \( \frac{\cos x}{\log x}, x>0 \)
Question 10. \( \cos (\log x + e^x), x>0 \)

NCERT EXERCISE 5.5 (Logarithmic Differentiation)

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

Question 1. \( \cos x. \cos 2x. \cos 3x \)

Question 2. \( \sqrt{ \frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)} } \)

Question 3. \( (\log x)^{\cos x} \)