Why is the derivative of x^5 equal to 5x^4?

The derivative of x^5 is 5x^4 because of the power rule for differentiation.

The power rule states that if we have a function of the form f(x) = x^n, where n is a constant, then the derivative of f(x) is given by:

f'(x) = n*x^(n-1)

In this case, we have f(x) = x^5, where n = 5. Applying the power rule, we get:

f'(x) = 5*x^(5-1)

       = 5*x^4

The power rule states that when differentiating a term with a variable raised to the power of n, the new power becomes n-1, and the coefficient is multiplied by the original power.

In the case of x^5, the new power becomes 5-1 = 4, and the derivative is 5*x^4.

Therefore, the derivative of x^5 is indeed 5x^4.

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