derivative of (x+4(e^2x))

Lösung

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

e^{2} (2 x + 4)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = x + 4, g = x

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

\frac{d}{d x} (x + 4) = 1

\frac{d x}{d x} = 1

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

Vereinfache

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

t an g e n t f (x) = \frac{2 x}{x ^{2} + 1}, at x = 1

\int 2 x (x^{2} + 5)^{3} d x

x \to - 1 lim (\frac{6 x + 5}{5 x - 6})

\frac{\partial}{\partial x} \frac{10 3 ( 5 x ) ^{2}}{3}

\frac{d y}{d x} - \frac{2 y}{x} = x^{- 1} y^{- 1}