Esercizio
$\frac{d}{dx}\left(\frac{sin^4\left(x\right)\cdot\left(3x+13\right)}{\sqrt{x^2+2}}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. Find the derivative d/dx((sin(x)^4(3x+13))/((x^2+2)^(1/2))). 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{\left(3x+13\right)\sin\left(x\right)^4}{\sqrt{x^2+2}}\right) e x=\frac{\left(3x+13\right)\sin\left(x\right)^4}{\sqrt{x^2+2}}. Applicare la formula: y=x\to \ln\left(y\right)=\ln\left(x\right), dove x=\frac{\left(3x+13\right)\sin\left(x\right)^4}{\sqrt{x^2+2}}. Applicare la formula: y=x\to y=x, dove x=\ln\left(\frac{\left(3x+13\right)\sin\left(x\right)^4}{\sqrt{x^2+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=4\ln\left(\sin\left(x\right)\right)+\ln\left(3x+13\right)- \left(\frac{1}{2}\right)\ln\left(x^2+2\right).
Find the derivative d/dx((sin(x)^4(3x+13))/((x^2+2)^(1/2)))
Risposta finale al problema
$\left(4\csc\left(x\right)\cos\left(x\right)+\frac{3}{3x+13}+\frac{-x}{x^2+2}\right)\frac{\left(3x+13\right)\sin\left(x\right)^4}{\sqrt{x^2+2}}$