Derivative Symbol

Derivative Symbol Derivative symbol is the notation for differentiation. The process of finding the derivative is called the differentiation. Derivative is a value based on some other asset. Derivative is a value that is derived from something else. Derivative based on different types of assets such as stock market, commodity, banks etc. For common function y = f(x) the derivative can be written as dy / dx. It is also denoted by f. the three notation of derivative are f, f and f. The main use of derivative is to minimize the risk while offering potential for high return to another. Example 1: Find the derivative of 2 sin (2 x) Solution: Derivative of 2 sin (2x) is written as d (2 sin (2x)) / dx Differentiate d (2 sin (2x)) / dx = 2 d (2 sin (2x)) / dx (by constant multiplication rule) = 2. 2 sin (2 x) = 4 cos (2 x) since 2*2 =4 and derivative of sin is cos. Example 2: Find the derivative of (x+1) / (x-2) Solution: Use the quotient rule for finding the derivative Quotient rule is (d/dx) (u/v) = v (d u/dx) u (d v/dx) / v2 (d/dx)(x+1) / (x-2), here u = (x+1) and v = (x-2) (d/dx)(x+1) / (x-2) = ((x-2) d(x+1)/dx (x+1) d(x-2)/dx) / (x-2)^2 = ((x-2) (1) (x+1) (1))/ (x-2)^2 ( use multiply rule of derivative) = x-2-x-1 / (x-2)^2 = -3 / (x-2)^2 Thus the derivative of (x+1) / (x-2) is -3 / (x-2)^2 The above example shows how to find the derivative of function using basic rules of derivative.