Find (d y)/(d x) if operatorname(Sec)^-1(x^2-1)

Question

Find (d y)/(d x) if operatorname(Sec)^-1(x^2-1)

Answer 1

To find

for \( \operatorname{Sec}^{-1}\left(x^{2}-1\right) \), we can use the chain rule and the derivative of the inverse secant function.The derivative of the inverse secant function is given by:

Now, let's apply the chain rule to find

:

Using the chain rule, we have:

where

.Now, let's find

:

Now, substitute

into the derivative of the inverse secant function:

Simplifying further, we get:

Therefore, the derivative of \( \operatorname{Sec}^{-1}\left(x^{2}-1\right) \) with respect to

is:

Question

Find (d y)/(d x) if operatorname(Sec)^-1(x^2-1)

Solution

Resposta