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Derivatan av $$$\frac{\sqrt{3} \sin{\left(u \right)}}{3}$$$
Relaterade kalkylatorer: Kalkylator för logaritmisk derivering, Räknare för implicit derivering med steg
Din inmatning
Bestäm $$$\frac{d}{du} \left(\frac{\sqrt{3} \sin{\left(u \right)}}{3}\right)$$$.
Lösning
Tillämpa konstantfaktorregeln $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$ med $$$c = \frac{\sqrt{3}}{3}$$$ och $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:
$${\color{red}\left(\frac{d}{du} \left(\frac{\sqrt{3} \sin{\left(u \right)}}{3}\right)\right)} = {\color{red}\left(\frac{\sqrt{3}}{3} \frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}$$Derivatan av sinus är $$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$:
$$\frac{\sqrt{3} {\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}}{3} = \frac{\sqrt{3} {\color{red}\left(\cos{\left(u \right)}\right)}}{3}$$Alltså, $$$\frac{d}{du} \left(\frac{\sqrt{3} \sin{\left(u \right)}}{3}\right) = \frac{\sqrt{3} \cos{\left(u \right)}}{3}$$$.
Svar
$$$\frac{d}{du} \left(\frac{\sqrt{3} \sin{\left(u \right)}}{3}\right) = \frac{\sqrt{3} \cos{\left(u \right)}}{3}$$$A