Differentiating hyperbolics
d(sinh x)/dx = cosh x; d(cosh x)/dx = sinh x; d(tanh x)/dx = sech² x.
Hyperbolic derivatives are clean: sinh and cosh swap. tanh derivative involves sech (= 1/cosh).
Worked examples
d/dx(sinh 2x) = 2 cosh 2x.
d/dx(cosh² x) = 2 cosh x sinh x = sinh 2x.
d/dx(arsinh x) = 1/√(x²+1).
Frequently asked questions
Reduces to trig forms?
Yes — via Osborn's rule. Useful integrals.
Why arsinh: integration form?
∫ 1/√(1+x²) dx = arsinh x + c. Hyperbolic forms simplify these integrals.