Übung
$\frac{d}{dx}\frac{\left(x^2-1\right)^3}{\left(1+2x\right)^5}$
Schritt-für-Schritt-Lösung
Learn how to solve problems step by step online. Find the derivative d/dx(((x^2-1)^3)/((1+2x)^5)). Wenden Sie die Formel an: \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}, wobei a=\left(x^2-1\right)^3 und b=\left(1+2x\right)^5. Simplify \left(\left(1+2x\right)^5\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 5 and n equals 2. Wenden Sie die Formel an: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), wobei a=3 und x=x^2-1. Wenden Sie die Formel an: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), wobei a=5 und x=1+2x.
Find the derivative d/dx(((x^2-1)^3)/((1+2x)^5))
Endgültige Antwort auf das Problem
$\frac{6\left(x^2-1\right)^{2}x\left(1+2x\right)^5-10\left(x^2-1\right)^3\left(1+2x\right)^{4}}{\left(1+2x\right)^{10}}$