Risolvere: $\frac{d}{dx}\left(\frac{x^3\cos\left(x\right)^3}{\sqrt{\left(x+1\right)^{3}}}\right)$
Esercizio
$\frac{dy}{dx}\left(\frac{x^3cos^3\left(x\right)}{\left(x+1\right)^{\frac{3}{2}}}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Find the derivative d/dx((x^3cos(x)^3)/((x+1)^(3/2))). 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{x^3\cos\left(x\right)^3}{\sqrt{\left(x+1\right)^{3}}}\right) e x=\frac{x^3\cos\left(x\right)^3}{\sqrt{\left(x+1\right)^{3}}}. Applicare la formula: y=x\to \ln\left(y\right)=\ln\left(x\right), dove x=\frac{x^3\cos\left(x\right)^3}{\sqrt{\left(x+1\right)^{3}}}. Applicare la formula: y=x\to y=x, dove x=\ln\left(\frac{x^3\cos\left(x\right)^3}{\sqrt{\left(x+1\right)^{3}}}\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=3\ln\left(x\right)+3\ln\left(\cos\left(x\right)\right)- \left(\frac{3}{2}\right)\ln\left(x+1\right).
Find the derivative d/dx((x^3cos(x)^3)/((x+1)^(3/2)))
Risposta finale al problema
$\left(\frac{3}{x}-3\tan\left(x\right)+\frac{-3}{2\left(x+1\right)}\right)\frac{x^3\cos\left(x\right)^3}{\sqrt{\left(x+1\right)^{3}}}$