(1) ${\displaystyle {\dfrac {dy}{dx}}=13x^{12}}$.

(2) ${\displaystyle {\dfrac {dy}{dx}}=-{\dfrac {3}{2}}x^{-{\frac {5}{2}}}}$.

(3) ${\displaystyle {\dfrac {dy}{dx}}=2ax^{(2a-1)}}$.

(4) ${\displaystyle {\dfrac {du}{dt}}=2.4t^{1.4}}$.

(5) ${\displaystyle {\dfrac {dz}{du}}={\dfrac {1}{3}}u^{-{\frac {2}{3}}}}$.

(6) ${\displaystyle {\dfrac {dy}{dx}}=-{\dfrac {5}{3}}x^{-{\frac {8}{3}}}}$.

(7) ${\displaystyle {\dfrac {du}{dx}}=-{\dfrac {8}{5}}x^{-{\frac {13}{5}}}}$.

(8) ${\displaystyle {\dfrac {dy}{dx}}=2ax^{a-1}}$.

(9) ${\displaystyle {\dfrac {dy}{dx}}={\dfrac {3}{q}}x^{\frac {3-q}{q}}}$.

(10) ${\displaystyle {\dfrac {dy}{dx}}=-{\dfrac {m}{n}}x^{-{\frac {m+n}{n}}}}$.

(1) ${\displaystyle {\dfrac {dy}{dx}}=3ax^{2}}$.

(2) ${\displaystyle {\dfrac {dy}{dx}}=13\times {\frac {3}{2}}x^{\frac {1}{2}}}$.

(3) ${\displaystyle {\dfrac {dy}{dx}}=6x^{-{\frac {1}{2}}}}$.

(4) ${\displaystyle {\dfrac {dy}{dx}}={\dfrac {1}{2}}c^{\frac {1}{2}}x^{-{\frac {1}{2}}}}$.

(5) ${\displaystyle {\dfrac {du}{dz}}={\dfrac {an}{c}}z^{n-1}}$.

(6) ${\displaystyle {\dfrac {dy}{dt}}=2.36t}$.

(7) ${\displaystyle {\dfrac {dl_{t}}{dt}}=0.000012\times l_{0}}$.

(8) ${\displaystyle {\dfrac {dC}{dV}}=abV^{b-1}}$, ${\displaystyle 0.98}$, ${\displaystyle 3.00}$ and ${\displaystyle 7.47}$ candle power per volt respectively.

(9) ${\displaystyle {\dfrac {dn}{dD}}=-{\dfrac {1}{LD^{2}}}{\sqrt {\dfrac {gT}{\pi \sigma }}},{\dfrac {dn}{dL}}=-{\dfrac {1}{DL^{2}}}{\sqrt {\dfrac {gT}{\pi \sigma }}}}$.
${\displaystyle \;\quad {\dfrac {dn}{d\sigma }}=-{\dfrac {1}{2DL}}{\sqrt {\dfrac {gT}{\pi \sigma ^{3}}}},{\dfrac {dn}{dT}}={\dfrac {1}{2DL}}{\sqrt {\dfrac {g}{\pi \sigma T}}}}$.