Question

find the derivative of The hyperbolic function with respect to x

Answer 1

Let u = x 2 and y = sinh u and use the chain rule to find the derivative of the given function f as follows. 
f '(x) = (dy / du) (du / dx) 
dy / du = cosh u, see formula above, and du / dx = 2 x 
f '(x) = 2 x cosh u = 2 x cosh (x 2) 
Substitute u = x 2 in f '(x) to obtain 
f '(x) = 2 x cosh (x 2)