d/dx (tan^-1 x + tan^-1 1/x ) =
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Step-by-step explanation:
The derivative of arctan(x) is defined as the (derivative of x)/(1 + x^2). For arctan(x), the derivative of x is 1, and the denominator is 1 + x^2, giving the answer of 1/(1+ x^2). For arctan(1/x), the derivative of 1/x is -1/x^2, and the denominator is 1 + 1/x^2, giving the answer of -1/(x^2)(1+(1/x^2)).
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