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Random Reddit Questions

Random Reddit Questions

The reddit question was, given that

$$x = t + \ln(\cosh t),\; y = \sinh t$$

Show that $$\frac{dy}{dx} = e^{-t}\cosh^2(t)$$

The "further maths" trick to the question is essentially recognising what $\sinh(t) + \cosh(t)$ is, which can either be remembered as an identity or derived from the exponential form of the hyperbolic functions. 

 

here's the solution to the first part.