Question

d/dt(v(t)=\sqrt{32t ^{2}}

Answer 1

are you looking for the anti derivative?

Answer 2

power rule of derivative

Answer 3

are you trying to differentiate
\[\sqrt{32t^2}\] or are you trying to find the function whose derivative is
\[\sqrt{32t^2}\]?

Answer 4

finding the function

Answer 5

in other words
\[\int\sqrt{32t^2}dt\]

Answer 6

\[\sqrt{32}=4\sqrt{2}\] so this is
\[4\sqrt{2}\int\sqrt{t^2}dt\]

Answer 7

or even
\[4\sqrt{2}\int |t|dt\]

Answer 8

do you know how to solve it?

Answer 9

so if t > 0 you get
\[2\sqrt{2}t^2\]

Answer 10

and if t < 0 you get
\[-2\sqrt{2}t^2\]

Answer 11

you can write this in one line if you put
\[2\sqrt{2}t \sqrt{t^2}\]

Answer 12

is that the power rule ?

Answer 13

THANK YOU SO MUCH