[elnino2206]

I understand how to integrate d[A]/dT = k[A] to form the integrated first - order rate equation: [A] = [A]0 * exp(-kt).

However to 'check' this by differentiating d[A]/dT to form k[A], I am having trouble.  So far I reach d[A]/dT = [A]0*-k*exp(-kt).  Please may someone point me in the right direction?

[mjc123]

Your rate equation should be d[A]/dt = -k[A] to give the quoted integral equation for [A]. This is the first order rate law. d[A]/dt = k[A] would be an autocatalytic reaction.