How does the power rule apply to calculate derivatives?
The power rule is a fundamental concept in calculus that helps you find the derivative of a function when you have a function in the form of f(x) = x^n, where n is a constant. Here's how it applies:
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Understanding the power rule: The power rule states that if you have a function
f(x) = x^n, then its derivativef'(x)is given byf'(x) = nx^(n-1). -
Applying the power rule: To apply the power rule, you simply multiply the exponent
nby the basexraised to the power of(n-1). For example, if you havef(x) = x^3, then applying the power rule gives youf'(x) = 3x^(3-1) = 3x^2.
Here's a simple breakdown:
- Original function:
f(x) = x^n - Derivative (using power rule):
f'(x) = nx^(n-1)