Esercizio
$\frac{d}{dx}\left(\frac{sin^2\left(x\right)tan^6\left(x\right)}{\left(x^2+2\right)^2}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Find the derivative d/dx((sin(x)^2tan(x)^6)/((x^2+2)^2)). Applicare la formula: \frac{d}{dx}\left(x\right)=y=x, dove d/dx=\frac{d}{dx}, d/dx?x=\frac{d}{dx}\left(\frac{\sin\left(x\right)^2\tan\left(x\right)^6}{\left(x^2+2\right)^2}\right) e x=\frac{\sin\left(x\right)^2\tan\left(x\right)^6}{\left(x^2+2\right)^2}. Applicare la formula: y=x\to \ln\left(y\right)=\ln\left(x\right), dove x=\frac{\sin\left(x\right)^2\tan\left(x\right)^6}{\left(x^2+2\right)^2}. Applicare la formula: y=x\to y=x, dove x=\ln\left(\frac{\sin\left(x\right)^2\tan\left(x\right)^6}{\left(x^2+2\right)^2}\right) e y=\ln\left(y\right). Applicare la formula: \ln\left(y\right)=x\to \frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\right), dove x=2\ln\left(\sin\left(x\right)\right)+6\ln\left(\tan\left(x\right)\right)-2\ln\left(x^2+2\right).
Find the derivative d/dx((sin(x)^2tan(x)^6)/((x^2+2)^2))
Risposta finale al problema
$\left(2\cot\left(x\right)+6\sec\left(x\right)\csc\left(x\right)+\frac{-4x}{x^2+2}\right)\frac{\sin\left(x\right)^2\tan\left(x\right)^6}{\left(x^2+2\right)^2}$