How do you find the derivative of u=2^(t^2)?

1 Answer
Dec 16, 2016

(du)/(dt)=2^(t(t+1))ln2

Explanation:

With functions like this use logarithmic differentiation.

Take logs to base ""e"" first, then differentiate.

u=2^(t^2)

lnu=ln2^(t^2)

using the laws of logs to simplify.

lnu=t^2ln2

differentiate with respect to ""t""

1/u(du)/(dt)=2tln2

rearrange

(du)/(dt)=u2tln2

substitute back for ""u""and tidy up.

(du)/(dt)=2^t2^(t^2)ln2

(du)/(dt)=2^(t^2+t)ln2

(du)/(dt)=2^(t(t+1))ln2