Funktion $$$- \frac{141 p t}{800} + \frac{1673}{500}$$$ derivaatta muuttujan $$$t$$$ suhteen

Summan/erotuksen derivaatta on derivaattojen summa/erotus:

$${\color{red}\left(\frac{d}{dt} \left(- \frac{141 p t}{800} + \frac{1673}{500}\right)\right)} = {\color{red}\left(- \frac{d}{dt} \left(\frac{141 p t}{800}\right) + \frac{d}{dt} \left(\frac{1673}{500}\right)\right)}$$

Sovella vakion kerroinsääntöä $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ käyttäen $$$c = \frac{141 p}{800}$$$ ja $$$f{\left(t \right)} = t$$$:

$$- {\color{red}\left(\frac{d}{dt} \left(\frac{141 p t}{800}\right)\right)} + \frac{d}{dt} \left(\frac{1673}{500}\right) = - {\color{red}\left(\frac{141 p}{800} \frac{d}{dt} \left(t\right)\right)} + \frac{d}{dt} \left(\frac{1673}{500}\right)$$

Sovella potenssisääntöä $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ käyttäen $$$n = 1$$$, toisin sanoen, $$$\frac{d}{dt} \left(t\right) = 1$$$:

$$- \frac{141 p {\color{red}\left(\frac{d}{dt} \left(t\right)\right)}}{800} + \frac{d}{dt} \left(\frac{1673}{500}\right) = - \frac{141 p {\color{red}\left(1\right)}}{800} + \frac{d}{dt} \left(\frac{1673}{500}\right)$$

Vakion derivaatta on $$$0$$$:

$$- \frac{141 p}{800} + {\color{red}\left(\frac{d}{dt} \left(\frac{1673}{500}\right)\right)} = - \frac{141 p}{800} + {\color{red}\left(0\right)}$$

Näin ollen, $$$\frac{d}{dt} \left(- \frac{141 p t}{800} + \frac{1673}{500}\right) = - \frac{141 p}{800}$$$.