Mastering The Power Rule: Finding Derivatives Of Power Functions

D of x^n

nx^n-1

The derivative of a function x^n is given by:

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

Here, n is a constant or an exponent. To obtain the derivative of x^n, we subtract 1 from the exponent and multiply the resulting term with the coefficient (n). Then the base (x) remains the same.

Let’s take an example to understand this formula more clearly:

Example:
Find the derivative of f(x) = x^4

Solution:
We can use the formula to find the derivative of the given function.

d/dx(x^4) = 4x^(4-1)
d/dx(x^4) = 4x^3

Therefore, the derivative of f(x) = x^4 is 4x^3.

Note that this formula applies to all power functions, regardless of the value of n.

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