calculating derivative with power rule

[Dorian Gray]

Greetings and Salutations Mathematicians,

I am struggling with these 3 problems involving derivatives and the power rule (we can ONLY use the power rule).




Even if you only have a suggestion for one of the three, it would certainly be appreciated. We just learned this today, and unfortunately our professor did not have enough time to show us how to do ones with items in the denominators.

Any comments, help, suggestions, advice, and/or wisdom is always welcomed.

Thanks again.

 

[Dorian Gray]

work

 

[Deleted member 4993]

Greetings and Salutations Mathematicians,

I am struggling with these 3 problems involving derivatives and the power rule (we can ONLY use the power rule).

View attachment 1691


Even if you only have a suggestion for one of the three, it would certainly be appreciated. We just learned this today, and unfortunately our professor did not have enough time to show us how to do ones with items in the denominators.

Any comments, help, suggestions, advice, and/or wisdom is always welcomed.

Thanks again.

Transform the given expressions to "powe" form (e.g.):

\(\displaystyle y \ = \ \frac{x^2 \ + \ 4x \ + \ 3}{\sqrt{x}} \ \)

\(\displaystyle = \ x^{\frac{3}{2}} \ + \ 4x^{\frac{1}{2}} \ + \ 3x^{-\frac{1}{2}}\)

Now apply "power" rule.....

 

[Dorian Gray]

is t his okay?

 

[medicalphysicsguy]

looks right

looks right to me