derivative of ax*e^{bx}

Lösung

\frac{d}{d x} (a x \cdot e^{b x})

a (e^{b x} + b e^{b x} x)

Schritte zur Lösung

\frac{d}{d x} (a x e^{b x})

Entferne die Konstante:

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

= a \frac{d}{d x} (x e^{b x})

Wende die Produktregel an:

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

f = x, g = e^{b x}

= a (\frac{d x}{d x} e^{b x} + \frac{d}{d x} (e^{b x}) x)

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

\frac{d}{d x} (e^{b x}) = e^{b x} b

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

Vereinfache

= a (e^{b x} + b e^{b x} x)

t an g e n t f (x) = (11 x - 1)^{- \frac{1}{5}}, at x = 3

\frac{\partial}{\partial x} (\frac{- y}{x ^{2} + y ^{2}})

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

d er i v a t i v e x^{- 9 c o s (x)}

\frac{d}{d x} (lo g_{e} (5 x))