Can you explain 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 an example of using the power rule?
Of course! If f(x) = x^3, then using the power rule, f'(x) = 3*x^(3-1) = 3x^2.
What if the exponent is negative?
Great question! If f(x) = x^(-2), then f'(x) = -2x^(-2-1) = -2x^(-3) or -2/x^3.
Are there any exceptions to the power rule?
Yes, the power rule doesn't apply to functions that aren't in the form of x^n, like trigonometric or exponential functions.
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