Let f(x) = 1 + x + x^{2} + x^{3} . Then the derivative is
D_{x}f(x) = 1 + 2x + 3x^{2} = (1+x)^{2} + 2x^{2}.
Thus, f is monotone on \mathbb{R} because

** A. ** f^{\prime} > 0

** B. ** f^{\prime} < 0

Hencef has an inverse function. Since f(x)\to\infty as
x\to\infty , and f(x)\to-\infty as x\to-\infty ,
it follows that the inverse function f^{-1} is defined for all numbers.

Find the derivative:

D_x \left( f^{-1} \right)(40) =

Hence

Find the derivative:

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