Derivative Problem Containing Square Root

[Jason76]

\(\displaystyle y = \dfrac{t - \sqrt{t}}{t^{1/7}}\)

\(\displaystyle y = \dfrac{t - t^{1/2}}{t^{1/7}}\)

\(\displaystyle y' = \dfrac{[t^{1/7}][\dfrac{d}{dx} (t - t^{1/2})] - [t - t^{1/2}][\dfrac{d}{dx} t^{1/7}]}{(t^{1/7})^{2}}\)

\(\displaystyle y' = \dfrac{[t^{1/7}][(1 - \dfrac{1}{2}(u)^{-1/2})] - [t - t^{1/2}][ \dfrac{1}{7}u^{-6/7}]}{(t^{1/7})^{2}}\)

\(\displaystyle y' = \dfrac{[t^{1/7}][(1 - \dfrac{1}{2}t^{-1/2})] - [t - t^{1/2}][ \dfrac{1}{7}t^{-6/7}]}{(t^{1/7})^{2}}\)

\(\displaystyle y' = \dfrac{(t^{1/7} - \dfrac{1}{2}t^{-5/14}) - (t^{1/7} - t^{-5/14})}{(t^{1/7})^{2}}\)

\(\displaystyle y' = \dfrac{t^{1/7} - \dfrac{1}{2}t^{-5/14} - t^{1/7} + t^{-5/14})}{(t^{1/7})^{2}}\)

 

[daon2]

First of all, fix your variables. I see t's u's and x's.

Your next step will be to combine like terms in the numerator and then factor out \(\displaystyle t^{-5/14}\) from the simplified numerator.