An function y=f(x) is defined implicitly by the formula x=tan(y), with the condition y epsilon (-pi/2, pi/2). Find and formula for its derivative, then obtain the formula for f'(x) in term of x alone.© BrainMass Inc. brainmass.com February 24, 2021, 2:21 pm ad1c9bdddf
We have x = tan(y) with y in the interval (-pi/2,pi/2)----(1)
Now, we can write, f(x) = y = tan^-1(x) ---Answer
This shows how to find the formula for the derivative of a given implicitly-defined function.