Understanding the Power Rule for Differentiation | Derivative of x^n Explained

d/dx[x^n]

The expression d/dx[x^n] represents the derivative of x raised to the power of n (where n is a constant)

The expression d/dx[x^n] represents the derivative of x raised to the power of n (where n is a constant).
To find the derivative of x^n, we can use the power rule of differentiation, which states that if we have a function of the form f(x) = x^n, then its derivative is given by:

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

In simpler terms, when we differentiate x^n, we bring down the exponent n as a coefficient, and reduce the exponent by 1.

So, the derivative of x^n with respect to x is n * x^(n-1).

For example, let’s consider finding the derivative of x^3:
Using the power rule, we have:

d/dx(x^3) = 3 * x^(3-1) = 3 * x^2

Therefore, the derivative of x^3 is 3x^2.

Note that this rule is applicable only when n is a constant. If n is a variable or a function of x, the derivative will be different and can be found using more advanced techniques like the chain rule or logarithmic differentiation.

More Answers: