Question

If f(x) = x tan^-1 x, find f'(1) from first principle.

Answer 1

Answer:

Step-by-step explanation:

f(x) = xtan^ -1x

Let x = u and tan^-1x = v

Applying d/dx(u/v) = u(d/dx)v+v(d/dx)u

f'(x) = d/dx(xtan^-1x)

x(d/dx)tan^-1x + tan^-1x(d/dx)x

x(1/1+x²) + tan^-1x(1)

∵ {(d/dx)tan^-1x = 1/1+x² and (d/dx)x = 1}

∴ x/1+x² + tan^-1x