Mastering The Power Rule: How To Differentiate Functions Of X^N Like A Pro

d/dx [x^n]

nx^n-1

To differentiate the function x^n with respect to x, we use the power rule of differentiation, which states that the derivative of x^n is given by:

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

Therefore, the derivative of x^n with respect to x is n times x raised to the power of n – 1.

For example, if we want to find the derivative of x^3 with respect to x, we use the power rule and get:

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

So, the derivative of x^3 with respect to x is 3x^2.

Similarly, if we want to find the derivative of x^5 with respect to x, we use the power rule and get:

d/dx [x^5] = 5 * x^(5-1) = 5x^4

So, the derivative of x^5 with respect to x is 5x^4.

In general, we can differentiate functions of the form x^n using the power rule, which applies to all real numbers n.

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