What are some examples of the power rule in calculus?
An example of an AI chatbot conversation about the power rule in calculus.
Can you explain the power rule in calculus?
Sure! The power rule states that if you have a function in the form of f(x) = x^n, the derivative f'(x) is n*x^(n-1).
Can you give me some examples of using the power rule?
Of course! For example, if f(x) = x^3, then f'(x) = 3*x^(3-1) = 3x^2.
What about a function like f(x) = 5x^4?
For f(x) = 5x^4, the derivative would be f'(x) = 4*5x^(4-1) = 20x^3.
Are there any exceptions to the power rule?
Yes, the power rule doesn't apply to functions where n is negative or a fraction, like f(x) = x^(-2) or f(x) = x^(1/2).
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