The slope of the line tangent to the curve y = arctan(4x) where x = 1/4 is 2
Given the function [tex]y = tan^{-1}4x[/tex]
The slope of the function can be given by differentiating the function as shown below;
On differentiating the given function
[tex]\frac{dy}{dx} =4[\frac{1}{(4x)^2+1} ]\\\frac{dy}{dx} =\frac{4}{(4x)^2+1} \\\frac{dy}{dx} =\frac{4}{16x^2+1} \\[/tex]
Substitute x = 1/4 into the result to have:
[tex]\frac{dy}{dx} =\frac{4}{16(1/4)^2+1} \\\frac{dy}{dx} =\frac{4}{(16/16)+1}\\\frac{dy}{dx} =\frac{4}{2}\\\frac{dy}{dx} =2[/tex]
Hence the slope of the line tangent to the curve y = arctan(4x) where x = 1/4 is 2
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