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Example: Solve Cosh Equation

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Wize University Calculus 1 Textbook > Derivatives

Hyperbolic Functions and their Derivatives

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Q:\bf{Q:} Solve for xx in the equation cosh⁡x=135\cosh x=\dfrac{13}{5} assuming x>0x>0.

More Hyperbolic Functions and their Derivatives Questions:
Derivatives: Hyperbolic Functions
Find the derivative of f(x)=ln⁡(sinh⁡(2x))f(x) = \ln(\sinh(2x))
Derivatives: Hyperbolic Functions
Q. Find the derivative of f(x)=ln⁡(sinh⁡(2x))f(x) = \ln(\sinh(2x))
Find the derivative of f(x)=sinh⁡(x2)cosh⁡(x)f(x) = \sinh(x^2)\cosh(x)
Hyperbolic Functions and Derivatives
Differentiate y=ln⁡(cosh⁡x)+12cosh⁡2xy=\ln(\cosh x)+\frac{1}{2\cosh^2 x} and simplify fully.
Hyperbolic Functions
Differentiate cosh⁡ln⁡x\cosh \ln x in two ways: by simplifying before taking the derivative, and by using the derivative of cosh⁡x\cosh x along with the chain rule.
Derivatives: Hyperbolic Functions
Find the derivative of f(x)=ln⁡(sinh⁡(2x))f(x) = \ln(\sinh(2x))
Find the derivative of f(x)=sinh⁡(x2)cosh⁡(x)f(x) = \sinh(x^2)\cosh(x)
Example: Solve Cosh Equation
Q:\bf{Q:} Solve for xx in the equation cosh⁡x=135\cosh x=\dfrac{13}{5} assuming x>0x>0.
Hyperbolic Functions and Derivatives
Differentiate y=ln⁡(cosh⁡x)+12cosh⁡2xy=\ln(\cosh x)+\dfrac{1}{2\cosh^2x} and simplify fully.
Find the derivative of f(x)=sinh⁡(x2)cosh⁡(x)f(x) = \sinh(x^2)\cosh(x)
Hyperbolic Functions
Prove the following identity:
cosh⁡2x−sinh⁡2x=1\cosh^2x-\sinh^2x=1
Find the derivative of f(x)=sinh⁡(x2)cosh⁡(x)f(x) = \sinh(x^2)\cosh(x)
Find the derivative of f(x)=ln⁡(sinh⁡(2x))f(x) = \ln(\sinh(2x))