Übung
$\frac{d}{dx}\left(x^{cot\left(x\right)-sin\left(x\right)}\right)$
Schritt-für-Schritt-Lösung
Learn how to solve problems step by step online. d/dx(x^(cot(x)-sin(x))). Wenden Sie die Formel an: \frac{d}{dx}\left(a^b\right)=y=a^b, wobei d/dx=\frac{d}{dx}, a=x, b=\cot\left(x\right)-\sin\left(x\right), a^b=x^{\left(\cot\left(x\right)-\sin\left(x\right)\right)} und d/dx?a^b=\frac{d}{dx}\left(x^{\left(\cot\left(x\right)-\sin\left(x\right)\right)}\right). Wenden Sie die Formel an: y=a^b\to \ln\left(y\right)=\ln\left(a^b\right), wobei a=x und b=\cot\left(x\right)-\sin\left(x\right). Wenden Sie die Formel an: \ln\left(x^a\right)=a\ln\left(x\right), wobei a=\cot\left(x\right)-\sin\left(x\right). Wenden Sie die Formel an: \ln\left(y\right)=x\to \frac{d}{dx}\left(\ln\left(y\right)\right)=\frac{d}{dx}\left(x\right), wobei x=\left(\cot\left(x\right)-\sin\left(x\right)\right)\ln\left(x\right).
Endgültige Antwort auf das Problem
$\left(\left(-\csc\left(x\right)^2-\cos\left(x\right)\right)\ln\left(x\right)+\frac{\cot\left(x\right)-\sin\left(x\right)}{x}\right)x^{\left(\cot\left(x\right)-\sin\left(x\right)\right)}$