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MathCalculus

Differentiation of 1/(1+x): Find the Derivative and Tangent Line at x = 2

The derivative of 1/(1+x) is −1/(x+1)². At x = 2, the point (2, 1/3) and slope −1/9 determine the tangent line.

Question

Use the limit definition of the derivative to find f′(x)f'(x) where

f(x)=1x+1.f(x)=\frac{1}{x+1}.

You may use differentiation rules to check your answer. Then find the equation of the tangent line to f(x)f(x) at x=2x=2.

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Evidence boundary

The target keyword is interpreted as 1/(1+x)1/(1+x), matching the verified source exercise. The result does not apply at x=−1x=-1, where the original function is undefined. The tangent-line result is specifically for x=2x=2.