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# Lecture - 6 Chapter 5 Continuity and Differentiability

*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}