Answer to Question #271912 in Calculus for Angel Nodado

Question

Find the first and second derivatives of the following and simplify whenever possible:

x = a cosh t; y=b sinh t

Answer 1

$y'_x = \dfrac{y'_t} {x'_t} = \dfrac{b \cosh t}{a\sinh t} = \dfrac{b} {a\tanh t}, \\ \\ y''_{xx} = \dfrac{(y' _x) '_t} {x'_t} = \dfrac{\frac{b}{a}\cdot \dfrac{\sinh^2t-\cosh^2t}{\sinh^2t} } {a\sinh t} = - \dfrac{b} {a^2\sinh^3t}.$