In Chapter 5, we have learnt how to find derivative of composite functions, inverse trigonometric functions, implicit functions, exponential functions and logarithmic functions.
👉 Learn how to find the derivative of exponential and logarithmic expressions. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the ...
It is advised that the reader plots this graph for particular values of b like 2, 3 and 4. Following are some of the salient features of the exponential functions: (1) Domain of the exponential function is R, the set of all real numbers. (2) Range of the exponential function is the set of all positive real numbers.
In the Introduction to the Derivative video we introduce the notion of the derivative of a function and explain how the derivative captures the instantaneous rate of change of a function. In the ...
- The following are exponential forms of some numbers? 10,000 = 10 4 (read as 10 raised to 4) 243 = 3 5, 128 = 2 7. Here, 10, 3 and 2 are the bases, whereas 4, 5 and 7 are their respective exponents. We also say, 10,000 is the 4th power of 10, 243 is the 5th power of 3, etc. 3. Numbers in exponential form obey certain laws, which are:
Remark The exponential series involving variable x can be expressed as Example 3 Find the coefficient of x2 in the expansion of e2x+3 as a series in powers of x. Solution In the exponential series = replacing x by (2x + 3), we get = Here, the general term is = . This can be expanded by the Binomial Theorem as Here, the coefficient of x2 is .