Question

Differentiate the function

Answer 1

2T^-1/4 power

Answer 2

@mathmale

Answer 3

With respect to \(T\)?

Answer 4

Yes.

Answer 5

\[\frac{d}{dt}\left[2T^{-1/4}\right]=2\frac{d}{dt}\left[T^{-1/4}\right]\]
Using the power rule, you have
\[2\frac{d}{dt}\left[T^{-1/4}\right]=2\left(-\frac{1}{4}\right)T^{-1/4~-~1}=-\frac{1}{2}T^{-5/4}\]