Übung
$\frac{d}{dx}\left(x^x\right)\frac{\sin\left(x\right)\cos\left(x\right)\tan^3\left(x\right)}{x}$
Schritt-für-Schritt-Lösung
Learn how to solve problems step by step online. d/dx(x^x(sin(x)cos(x)tan(x)^3)/x). Vereinfachen Sie die Ableitung durch Anwendung der Eigenschaften von Logarithmen. Wenden Sie die Formel an: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), wobei d/dx=\frac{d}{dx}, ab=x^{\left(x-1\right)}\sin\left(x\right)\cos\left(x\right)\tan\left(x\right)^3, a=\sin\left(x\right), b=x^{\left(x-1\right)}\cos\left(x\right)\tan\left(x\right)^3 und d/dx?ab=\frac{d}{dx}\left(x^{\left(x-1\right)}\sin\left(x\right)\cos\left(x\right)\tan\left(x\right)^3\right). Wenden Sie die Formel an: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), wobei d/dx=\frac{d}{dx}, ab=x^{\left(x-1\right)}\cos\left(x\right)\tan\left(x\right)^3, a=\cos\left(x\right), b=x^{\left(x-1\right)}\tan\left(x\right)^3 und d/dx?ab=\frac{d}{dx}\left(x^{\left(x-1\right)}\cos\left(x\right)\tan\left(x\right)^3\right). Wenden Sie die Formel an: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), wobei d/dx=\frac{d}{dx}, ab=x^{\left(x-1\right)}\tan\left(x\right)^3, a=\tan\left(x\right)^3, b=x^{\left(x-1\right)} und d/dx?ab=\frac{d}{dx}\left(x^{\left(x-1\right)}\tan\left(x\right)^3\right).
d/dx(x^x(sin(x)cos(x)tan(x)^3)/x)
Endgültige Antwort auf das Problem
$x^{\left(x-1\right)}\cos\left(x\right)^2\tan\left(x\right)^3+\sin\left(x\right)\left(-x^{\left(x-1\right)}\sin\left(x\right)\tan\left(x\right)^3+\cos\left(x\right)\left(3x^{\left(x-1\right)}\tan\left(x\right)^{2}\sec\left(x\right)^2+\left(\ln\left(x\right)+\frac{x-1}{x}\right)x^{\left(x-1\right)}\tan\left(x\right)^3\right)\right)$