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.