Differentiation of x^n | differention of x to the power n | derivative of x^n

differentiation of x^n | differentiation of e power x | derivative of x^n

The differentiation of x^n with respect to x is given by:

d/dx (x^n) = n*x^(n-1)

Here, n is any real number (positive, negative, or zero) and x is the variable with respect to which we are differentiating.

For example:

If n = 2, then d/dx (x^2) = 2*x^(2-1) = 2x
If n = 3, then d/dx (x^3) = 3*x^(3-1) = 3x^2
If n = -1, then d/dx (x^-1) = -x^(-1-1) = -x^(-2) = -1/x^2
If n = 1/2, then d/dx (x^(1/2)) = (1/2)*x^((1/2)-1) = (1/2)x^(-1/2) = 1/(2x^(1/2))

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