Inverse Hyperbolic Functions Quiz

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Questions and Answers

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 (A)

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

Flashcards

Derivative of sinh⁻¹(F(x))

The derivative of the inverse hyperbolic sine of F(x) is F'(x) divided by the square root of 1 plus F(x) squared.

Derivative of cosh⁻¹(F(x))

The derivative of the inverse hyperbolic cosine of F(x) is F'(x) divided by the square root of F(x) squared minus 1.

Derivative of tanh⁻¹(F(x))

The derivative of the inverse hyperbolic tangent of F(x) is F'(x) divided by 1 minus F(x) squared.

Power Rule Example

x² * x³ = x⁵ ; (x²)³ = x⁶

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Derivative of coth⁻¹(F(x))

The derivative of the inverse hyperbolic cotangent of F(x) is F'(x) divided by one minus F(x) squared.

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