Esercizio
$\frac{d}{dx}\left(\frac{\left(x^3+1\right)^4sin^2x}{x^{\frac{1}{3}}}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di calcolo integrale passo dopo passo. Find the derivative d/dx(((x^3+1)^4sin(x)^2)/(x^(1/3))). 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{\left(x^3+1\right)^4\sin\left(x\right)^2}{\sqrt[3]{x}}\right) e x=\frac{\left(x^3+1\right)^4\sin\left(x\right)^2}{\sqrt[3]{x}}. Applicare la formula: y=x\to \ln\left(y\right)=\ln\left(x\right), dove x=\frac{\left(x^3+1\right)^4\sin\left(x\right)^2}{\sqrt[3]{x}}. Applicare la formula: y=x\to y=x, dove x=\ln\left(\frac{\left(x^3+1\right)^4\sin\left(x\right)^2}{\sqrt[3]{x}}\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=4\ln\left(x^3+1\right)+2\ln\left(\sin\left(x\right)\right)- \left(\frac{1}{3}\right)\ln\left(x\right).
Find the derivative d/dx(((x^3+1)^4sin(x)^2)/(x^(1/3)))
Risposta finale al problema
$\left(\frac{12x^{2}}{\left(x+1\right)\left(x^{2}-x+1\right)}+2\csc\left(x\right)\cos\left(x\right)+\frac{-1}{3x}\right)\frac{\left(x^3+1\right)^4\sin\left(x\right)^2}{\sqrt[3]{x}}$