Risolvere: $\frac{d}{dx}\left(y=\frac{1}{\left(2x^2+x\right)^3}\right)$
Esercizio
$\frac{dy}{dx}\left(y=\frac{1}{\left(2x^2+x\right)^3}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(y=1/((2x^2+x)^3)). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=y e b=\frac{1}{\left(2x^2+x\right)^3}. Applicare la formula: \frac{d}{dx}\left(x\right)=1. 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=1 e b=\left(2x^2+x\right)^3. Simplify \left(\left(2x^2+x\right)^3\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals 2.
Risposta finale al problema
$y^{\prime}=\frac{-3\left(4x+1\right)}{\left(2x^2+x\right)^{4}}$