Find the derivative of the function.

Question

f(x) = arctan (x/a)

Answer 1

Use implicit differentiation:

y=arctan(x/a)
tan(y)=x/a
sec²(y)*dy/dx = 1/a
dy/dx = (1/a)/sec²(x)
=(1/a)/(1+tan²(x))
=(a/a²)/(1+(x/a)²)
=a/(a²+x²)