nth Derivative of Root x
nth derivative of root x is finding the derivative of root x successively n times. If we differentiate any function two times successively then it is called second order derivative. In this manner, if we differentiate any function n times successively we call it nth order derivative
let f(x) = βx = x1/2
β f'(x) = 1/2(x)1/2 β 1
β fβ(x) = 1/2(1/2 β 1)(x)1/2 β 1 β 1 = 1/2(1/2 β 1)(x)1/2 β 2
β fβ'(x) = 1/2(1/2 β 1)(1/2 β 1 β 1)(x)1/2 β 1 β 1 β 1 = 1/2(1/2 β 1)(1/2 β 1 β 1)(x)1/2 β 3
Based on the above pattern, the nth derivative of root x is given as
β fn(x) = 1/2(1/2 β 1)β¦β¦(1/2 β (n β 1))(x)1/2 β n
Derivative of Root x
Derivative of Root x is (1/2)x-1/2 or 1/(2βx). In general, the derivative of a function is defined as the change in the dependent variable, i.e. y = f(x) with respect to the independent variable, i.e. x. This process, also known as differentiation in calculus. Root x is an abbreviation used for the square root function which is mathematically represented as βx or x1/2 (x raised to the power half).
In this article, we will discuss the derivative in math, the derivative of root x, various methods to derive it including the first principle method and the power rule, some solved examples, and practice problems.