Question

Differentiate the function!

Answer 1

\[2t ^{-1/4}\]

Answer 2

If we need the derivative all we need to do is apply the power rule here

Answer 3

I know that is

Answer 4

-1/2t?

Answer 5

-1/2 sqrt (t)

Answer 6

So anytime it is raised to a fraction power, I need to sqrt? I am self taught in this calc class.

Answer 7

\[\large nx^{n - 1}\]

So we know that here 'n' = -1/4

So differentiating we have

\[\large -\frac{t^{-\frac{1}{4} - 1}}{2}\]
\[\large -\frac{t^{5/4}}{2}\]
\[\large -\frac{1}{2t^{5/4}}\]

Answer 8

Ohh. Ok. Thanks.

Answer 9

No not at all!

for derivatives it is actually best to make the square root an exponent as you have here!

Answer 10

For example...with your original question here...we COULD have

\[\large \frac{2}{\sqrt[4]{t}}\]

But instead, we change that radical to an exponent and make your equation

\[\large 2t^{-1/4}\]

Always easier to make it an exponent

Answer 11

Because as you saw...the power rule makes it quick and easy to do

Answer 12

Thanks so much! Im screen shooting this!

Answer 13

No problem!