In session 15 recitation video (Graphing the Arctan Function), can you guys tell me the detailed solution of using \frac{d}{dx} an{x} = \sec^{2} x to find the slope of the graph, which is 1? (In the video, the part is around 1:40 to 2:00)

Question

In session 15 recitation video (Graphing the Arctan Function), can you guys tell me the detailed solution of using \frac{d}{dx} 	an{x} = \sec^{2} x  to find the slope of the graph, which is 1? (In the video, the part is around 1:40 to 2:00)

anonymous · Answer

Not sure what you are asking? How to find the derivative of tan x?
Why is he taking the derivative of tanx?

anonymous · Answer

I mean, how he uses:$$\large \frac{d}{dx} \tan{x} = \sec^{2} x$$which I know how to find, to get the slope of 1. (He is taking derivative to find the slope of the tan x) How does he get the value of 1?

anonymous · Answer

Hes, finding the tangent to the curve of tan x at the point 0 so
$$f'(0)= \sec^2(0)=\frac{1}{cos^2(0)}=\frac{1}{1}=1$$

anonymous · Answer

Nice! Thank you.