A) ${\displaystyle \ \ {\frac {3}{5\ v^{3}}}={\frac {3}{5}}\ v^{-3}\ \Rightarrow \ }$
${\displaystyle \qquad b(v)=7\ \sin v-\ln v+{\frac {3}{5}}\ v^{-3}+3\ \Rightarrow \ }$
${\displaystyle \qquad b'(v)=7\cos v-{\frac {1}{v}}-{\frac {9}{5}}\ v^{-4}}$

${\displaystyle \qquad b(2{,}4)\approx 6{,}90\qquad b'(2{,}4)\approx -2{,}45}$

B) ${\displaystyle \ \ {\frac {5}{\sqrt[{4}]{t^{3}}}}={5}\ t^{-{\frac {3}{4}}}\ \Rightarrow \ }$
${\displaystyle \qquad v(t)={5}\ t^{-{\frac {3}{4}}}-\cos t+t-t^{-3}\ \Rightarrow \ }$
${\displaystyle \qquad v'(t)={-{\frac {15}{4}}}\ t^{-{\frac {7}{4}}}+\sin t+1+3\ t^{-4}\ }$

${\displaystyle \qquad v(2{,}4)\approx 5{,}66\qquad v'(2{,}4)\approx -1{,}15}$

C) ${\displaystyle \ \ {\sqrt[{3}]{\frac {27}{b^{7}}}}={3}\ t^{-{\frac {7}{3}}}\ \Rightarrow \ }$
${\displaystyle \qquad t(b)=5\ e^{b}-{3}\ b^{-{\frac {7}{3}}}+\tan b\quad }$
${\displaystyle \qquad t'(b)=5\ e^{b}+{7}\ b^{-{\frac {10}{3}}}+{\frac {1}{\cos ^{2}b}}\quad }$

${\displaystyle \qquad t(2{,}4)\approx 53{,}8\qquad t'(2{,}4)\approx 57{,}3}$