Esercizio
$\frac{d}{dt}\left(\frac{\sqrt{t-4}}{tcos\left(t\right)}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Find the derivative d/dt(((t-4)^(1/2))/(tcos(t))). Applicare la formula: \frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}, dove a=\sqrt{t-4} e b=t\cos\left(t\right). Applicare la formula: \left(ab\right)^n=a^nb^n. Applicare la formula: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dt}, ab=t\cos\left(t\right), a=t, b=\cos\left(t\right), dx=dt e d/dx?ab=\frac{d}{dt}\left(t\cos\left(t\right)\right). Applicare la formula: -\left(a+b\right)=-a-b, dove a=\frac{d}{dt}\left(t\right)\cos\left(t\right), b=t\frac{d}{dt}\left(\cos\left(t\right)\right), -1.0=-1 e a+b=\frac{d}{dt}\left(t\right)\cos\left(t\right)+t\frac{d}{dt}\left(\cos\left(t\right)\right).
Find the derivative d/dt(((t-4)^(1/2))/(tcos(t)))
Risposta finale al problema
$\frac{\frac{t\cos\left(t\right)}{2\sqrt{t-4}}+\sqrt{t-4}\left(-\cos\left(t\right)+t\sin\left(t\right)\right)}{t^2\cos\left(t\right)^2}$