`h(t) = cot^-1(t) + cot^-1(1/t)` Find the derivative of the function. Simplify where possible.

Textbook Question

Chapter 3, 3.5 - Problem 55 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`d/(dx) cot^-1x=(-1)/(1+x^2)`

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

`h'(t)=(-1)/(1+t^2) + (-1)/(1+(1/t)^2) *d/(dt) (1/t)`

`h'(t)=(-1)/(1+t^2) + (-1)/(1+(1/t)^2) *(-1t^-2)`

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

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

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

`h'(t)=0`

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