Question

What is the Derivative of t^(3/2) (2+t^(1/2))

Answer is 3t^(1/2)+2t
I can't seem to get it.

Answer 1

you have two functions of 't', are you using the product?

Answer 2

or multiply through the brackets and use exponent rules before taking the derivative.
Which way have you tried?

Answer 3

All the ways I guess lol
Wait so I multiply t^(3/2) through the parens first?

Answer 4

yes, you can approach it that way...it leads to two terms, each a straight derivative.

Answer 5

ok wait what do you get for the first step
2t^(3/2)+t^(4/2)?

Answer 6

Damn I got it now! THanks soo much

Answer 7

I thought we are supposed to do whats inside the parens first?

Answer 8

any algebraic steps you do to the function don't alter it in any way, so sometimes its just a matter of massaging into into the most convenient form

Answer 9

alternately, if you were to go directly from the form given:
\[\huge f(t)=t^{\frac{3}{2}}(2+t^{\frac{1}{2}})\]
\[\huge f'(t)=uv'+u'v\]
\[u=t^{\frac{3}{2}}\]
\[u' = \frac{3}{2}t^{\frac{1}{2}}\]
\[v=2+t^{\frac{1}{2}}\]
\[v'=\frac{1}{2}t^{-\frac{1}{2}}\]

Answer 10

ok thank you