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Implicit differentiation

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.

Solution Preview

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

We ...

Solution Summary

This shows how to find the formula for the derivative of a given implicitly-defined function.