Find the derivative of the function. h(t) = 3 cot^-1(t) + 3 cot^-1(1/t)

Question

Find the derivative of the function.

h(t) = 3 cot^-1(t) + 3 cot^-1(1/t)

Answer 1

Greetings! Lets solve this !

So, note that d/dt (cot^-1t) = -1/ (1+t²)

Then,

h' (t) = 3 ( -1 / (1+t²) ) + 3 ( -1 / (1+(t^-1)²) ) (-t^-2)

= -3 / (1+t²) + 3t^-2 / (1+(t^-1)²

I hope this helps!