Inverse Hyperbolic Functions Quiz

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What is the derivative of the inverse hyperbolic function $sinh^{-1} F(X)$?

$rac{F'(X)}{ig(1 - (F(X))^2ig)}$

$rac{F'(X)}{ig(1 + (F(X))^2ig)^{1/2}}$

$rac{-F'(X)}{F(X)ig(ig|1 - (F(X))^2ig|ig)^{1/2}}$

$rac{F'(X)}{ uig(1 + (F(X))^2ig)}$ (correct)

The derivative of $sech^{-1} F(X)$ is $rac{-F'(X)}{N(F(X) imes ext{sqrt}(1 - (F(X))^2))}$.

True

What is the result of $(x^2)^3$?

x^6

The derivative of $tanh^{-1} F(X)$ is $rac{F'(X)}{1 - (F(X))^2}$ and is applicable when $F(X)$ is _____ either -1 or 1.

<p>not</p> Signup and view all the answers

Match the following inverse hyperbolic functions with their derivatives:

<p>sinh^{-1} F(X) = $rac{F'(X)}{ ext{sqrt}(1 + (F(X))^2)}$ cosh^{-1} F(X) = $rac{F'(X)}{ ext{sqrt}((F(X))^2 - 1)}$ tanh^{-1} F(X) = $rac{F'(X)}{1 - (F(X))^2}$ sech^{-1} F(X) = $rac{-F'(X)}{F(X) ext{sqrt}(1 - (F(X))^2)}$</p> Signup and view all the answers