U substitution for differentiation?

[kurious]

How do I evaluate:

d/dt sqrt [ t^4 + t^2 ]= 0
to get a max/min value.

can I make a u substitution of some sort?

 

[HallsofIvy]

Yes, that's basically just the "chain rule".

Let u= t⁴+ t²

then d sqrt(t⁴+ t²)/dt= d u^1/2/du* du/dt
= (1/2)u^-1/2 * (4t³+ 2t)
= (1/2)(t⁴+t²)^-1/2)*(4t³+ 2t)

 

[kurious]

Thanks for your help.