Question

hallar la derivada de: s(t)=t^3(2/t-3/t^2)^2​

Answer 1

$S_{(t)} =t^{3}(\frac{2}{t}-\frac{3}{t^{2} }  )^{2}  \\S_{(t)} =t^{3}(\frac{4}{t^{2} }+\frac{9}{t^{4} }-2.\frac{2}{t} .\frac{3}{t^{2} }   )\\S_{(t)} =t^{3}(\frac{4}{t^{2} }+\frac{9}{t^{4} } -\frac{12}{t^{3} }  )\\S_{(t)} =4t+9t^{-1} -12\\derivando\\S_{(t)} ^{|} =4-9t^{-2}$