derivative of e^{2x}(2x+1)

Lösung

\frac{d}{d x} (e^{2 x} (2 x + 1))

4 e^{2 x} x + 4 e^{2 x}

Schritte zur Lösung

\frac{d}{d x} (e^{2 x} (2 x + 1))

Wende die Produktregel an:

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

f = e^{2 x}, g = 2 x + 1

= \frac{d}{d x} (e^{2 x}) (2 x + 1) + \frac{d}{d x} (2 x + 1) e^{2 x}

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

\frac{d}{d x} (2 x + 1) = 2

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

Vereinfache

e^{2 x} \cdot 2 (2 x + 1) + 2 e^{2 x} : 4 e^{2 x} x + 4 e^{2 x}

= 4 e^{2 x} x + 4 e^{2 x}

h \to 0 lim (\frac{49 + h - 7}{h})

l a pl a ce t r an s f or m 2 \cdot sin (3 t)

a re a y = e^{3 x}, y = e^{- 3 x}, x = - 1

\int_{0}^{2} - 6 x^{3} x^{2} + 4 d x

\frac{d}{d x} (1 + x + 5 x^{2})