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5. Let f(x) = arctan(In x) for all x >0. A graph of y = f(x) is shown in the figure. (a) Find the formula for the derivative

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f(x)= arctan (hux) x 70 = tant (mx), x70 @ f(x)=d tant ( mx) 1 (mm) U da It (mx)2 Chlmx)=jú 1 x{1+[mx)} then we If we assum. f is continuous on [x1, 2] f is differentiable on (12) f(x1) = f (22) So, there exists atleast one point o such that > f(ctana The graph of e g(x), HE(-712, 7/2). y=etanx ده) -12 1/2 tan(o) re f(o)= et = eo =1 4 f() - 2 (1 + (0)2 = 1 1 (f) (0) f

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