Funktion $$$\cos{\left(t \right)} + 1$$$ derivaatta
Aiheeseen liittyvät laskurit: Logaritmisen derivoinnin laskin, Vaiheittainen implisiittisen derivoinnin laskin
Syötteesi
Määritä $$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right)$$$.
Ratkaisu
Summan/erotuksen derivaatta on derivaattojen summa/erotus:
$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right) + \frac{d}{dt} \left(1\right)\right)}$$Vakion derivaatta on $$$0$$$:
$${\color{red}\left(\frac{d}{dt} \left(1\right)\right)} + \frac{d}{dt} \left(\cos{\left(t \right)}\right) = {\color{red}\left(0\right)} + \frac{d}{dt} \left(\cos{\left(t \right)}\right)$$Kosinin derivaatta on $$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$:
$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)} = {\color{red}\left(- \sin{\left(t \right)}\right)}$$Näin ollen, $$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right) = - \sin{\left(t \right)}$$$.
Vastaus
$$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right) = - \sin{\left(t \right)}$$$A
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