 Hi and welcome to the session. Today we will learn about derivatives of exponential and logarithmic functions. First of all let us see what is a exponential function. Let B be a real number such that B is greater than 1 then f of x equal to B to the power x is called the exponential function. The domain of exponential function is the set of real numbers and its range is the set of positive real numbers. B is called the base of the exponential function B to the power x. So exponential function with base 10 that is f of x is equal to 10 to the power x is known as common exponential function and the exponential function with base e that is f of x equal to e to the power x is known as natural exponential function. One striking property of natural exponential function in differential calculus is that it does not change during the process of differentiation. So that means d by dx of e to the power x is equal to e to the power x itself. Let us move on to logarithmic function let B be a real number B is greater than 1 then log of a to the base B is equal to x if B to the power x is equal to a. So this is known as logarithmic function. Now domain of logarithmic function is the set of all positive real numbers and its range is the set of all real numbers. Logarithmic function to the base 10 that is log of a to the base 10 is known as common logarithm of a. Logarithmic function to the base e that is log a to the base e is natural logarithm of a and log a to the base e is simply denoted by log a. Now let's see few results related to logarithmic functions. There is a standard change of base rule to obtain log p to the base a in terms of log p to the base b that is log p to the base a is equal to log p to the base b upon log a to the base b. Second result is log to the base b is equal to log p to the base b plus log q to the base b. Third result is log of p to the power n to the base b is equal to n into log p to the base b and the fourth one is log of x upon y to the base b is equal to log x to the base b minus log y to the base b. Now the derivative of log x that is d by dx of log x is equal to 1 upon x. Let's see some examples. Here we are given f of x equal to e to the power x to the power 2 and we need to find f dash of x that is derivative of f of x. So f dash of x is equal to d by dx of e to the power x to the power 2. Now we know that derivative of e to the power x is e to the power x itself. So this will be equal to e to the power x to the power 2 into d by dx of x to the power 2 using chain rule and this will be equal to e to the power x to the power 2 into 2x. So f dash of x is equal to 2x into e to the power x to the power 2. Let's take one more example. Here f of x is given by log of sin x and we need to find f dash of x. So here f dash of x is equal to d by dx of log of sin x. Now we already know that d by dx of log x is 1 upon x. So here in place of x we have sin x. So this will be equal to 1 upon sin x into d by dx of sin x using chain rule which will be equal to 1 upon sin x into derivative of sin x is cos x. So this is equal to cos x over sin x that is cot x. Thus f dash of x is equal to cot x. Thus in this session we have learned the derivatives of exponential and logarithmic functions and with this we finished this session. Hope you must have understood all the concepts. Goodbye, take care and have a nice day.