Question

find f'(t) for f(t)= (3^2t)/t

Answer 1

Mmmm quotient rule :)

Answer 2

\[\Large\bf\sf f(t)=\frac{3^{2t}}{t}\]
\[\Large\bf\sf f'(t)=\frac{\color{royalblue}{\left(3^{2t}\right)'}t-3^{2t}\color{royalblue}{\left(t\right)'}}{t^2}\]

Answer 3

Differentiate \(\Large\bf\color{royalblue}{\text{ these parts}}\).

Answer 4

Remember how to take the derivative of an exponential function?\[\Large\bf\sf (3^{2t})'\quad=\quad ?\]

Answer 5

\[\frac{ 3^{2t} }{ t }(2\ln3-\frac{ 1 }{ t })\]