Can you help me find the derivative of this? Please (cot^-1(sqrtt))

1 Answer
Nov 19, 2017

[ 1 / (2sqrt(t)(t + 1) } ]

Explanation:

We need to differentiate d/dt [ "arccot"(sqrt(t))]

We use the Chain Rule to solve the problem.

Chain Rule states that .....

d/dx[f{g(x)}] = f'{g(x)}g'(x) to solve the problem.

Chain Rule can also be expressed as ......

dy/(dx) = (dy)/(du)*(du)/(dx)

So we have

d/(dt){"arccot"(sqrt(t))} = d/(du){"arccot"(u)}(du)/(dt)

we assume that u = sqrt(t)

Hence, we obtain

d/(du){"arccot"(u)} = -1/(1 + u^2)

= d/(dt) {sqrt(t)} / (1 + t)

Using Power Rule, we obtain the following:

d/(dt) sqrt(t) = d/(dt){t ^ (1/2)}

= t^(-1/2)/2

We will now write the final solution to our problem as follows:

d/(dt){"arccot"(sqrt(t))} = 1/{2 sqrt(t) (t+1)}

This is our final answer.