Answer:
[tex]\huge\boxed{j.\frac{a}{-x^2}}[/tex]
[tex]\huge\boxed{l.1 + \frac{1}{\frac{1}{2}\sqrt{x}}}[/tex]
[tex]\huge\boxed{n.\frac{a}{\frac{-1}{2}\sqrt{x}}}[/tex]
Step-by-step explanation:
This problem can be solved simply by utilizing the power rule: [tex]\frac{d}{dx}x^n =nx^{n-1}[/tex].
j. [tex]x^{-1}(ax+b)[/tex] --> [tex]-1x^{-2}(a)[/tex] -->[tex]\frac{a}{-x^2}[/tex]
l. [tex]x + x^{\frac{1}{2}}[/tex] --> [tex]1 + \frac{1}{2}x ^ {\frac{-1}{2}}[/tex] --> [tex]1 + \frac{1}{\sqrt{x}}[/tex]
n. [tex]x^{\frac{1}{2}}(ax+b)[/tex] --> [tex]x^{-\frac{3}{2}}(a)[/tex] --> [tex]\frac{a}{\frac{-1}{2}\sqrt{x}}[/tex]
Hope it helps :) and let me know if you want me to elaborate.
