derivative of e^{2x}ln(3x)

Lösung

\frac{d}{d x} (e^{2 x} ln (3 x))

2 e^{2 x} ln (3 x) + \frac{e ^{2 x}}{x}

Schritte zur Lösung

\frac{d}{d x} (e^{2 x} ln (3 x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{2 x}, g = ln (3 x)

= \frac{d}{d x} (e^{2 x}) ln (3 x) + \frac{d}{d x} (ln (3 x)) e^{2 x}

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

= e^{2 x} \cdot 2 ln (3 x) + \frac{1}{x} e^{2 x}

\frac{1}{x} e^{2 x} = \frac{e ^{2 x}}{x}

= 2 e^{2 x} ln (3 x) + \frac{e ^{2 x}}{x}

\frac{d}{d x} (x^{3} + 4 x^{2} + 2)

\frac{d}{d x} (x^{5} - 4 x^{3})

\frac{d ^{2}}{d x ^{2}} (19 e^{x^{2}})

\frac{d y}{d x} = 5 (y - 2)^{\frac{3}{5}}

\frac{d y}{d x} + 6 x^{2} y = - 3 x^{2}