derivative of 1/x
To find the derivative of the function f(x) = 1/x, we can use the power rule for differentiation
To find the derivative of the function f(x) = 1/x, we can use 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, the derivative of f(x) with respect to x is given by f'(x) = n * x^(n-1).
In this case, our function is f(x) = 1/x, which can be rewritten as f(x) = x^(-1). Using the power rule, we can differentiate f(x) as follows:
f'(x) = (-1) * x^(-1-1)
= -1 * x^(-2)
= -1/x^2.
Therefore, the derivative of 1/x with respect to x is -1/x^2.
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