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Question

Determine the derivative dzdt\frac{\mathrm{dz}}{\mathrm{dt}} and﻿dzdt∣t=3\left. \frac{dz}{dt} \right|_{t=3}dtdz​​t=3​﻿ for the function z=t+2t+3 z = \frac{t+2}{t+3} .

Accepted Answer

dzdt=1(t+3)2 \frac{dz}{dt} = \frac{1}{$$(t+3)^2$$} ; dzdt∣t=3=136 \left. \frac{dz}{dt} \right|_{t=3} = \frac{1}{36}

Answer

dzdt=3(t+3)2\frac{dz}{dt}=\frac{3}{$$(t+3)^2$$}; dzdt∣t=3=112\left.\frac{dz}{dt}\right|_{t=3}=\frac{1}{12}

Answer

dzdt=3(t+3)2\frac{dz}{dt}=\frac{3}{$$(t+3)^2$$}; dzdt∣t=3=136 \left. \frac{dz}{dt} \right|_{t=3} = \frac{1}{36}

Answer

dzdt=1(t+3)2 \frac{dz}{dt} = \frac{1}{$$(t+3)^2$$} ; dzdt∣t=3=19\left.\frac{dz}{dt}\right|_{t=3}=\frac19

Determine the derivative dzdt\(\frac{\mathrm{dz}\)}{\(\mathrm{dt}\)} anddzdt∣t=3\(\left\). \(\frac{dz}{dt}\) \(\right\)|_{t=3}dtdzt=3 for the function z=t+2t+3 z = \(\frac{t+2}{t+3}\) .

Determine the derivative $\frac{d z}{d t}$ and $\(\left\). \(\frac{dz}{dt}\) \(\right\)|_{t=3}$ for the function $z = \frac{t + 2}{t + 3}$ .