Calculus problem read description

Question

Let f(x) = tan(x), and assume that you only know d/dx(arctan(x))= (1/(1+x^2)). You may NOT use the fact that you probably already know d/dx (f(x))! Use our “inverse function derivative” process to find d/dx(f(x))

Answer 1

f(x) = tan(x)

x = tan^-1(f(x))

Take d/dx of both sides

1 = 1/(1+(f(x))²) df(x)/dx by chain rule

df(x)/dx = 1 + (f(x))² = 1+ tan²(x) = sec²(x)