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

Lösung

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

e^{x} x^{2} + 4 e^{x} x + 3 e^{x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 (x + 1) e^{x} + e^{x} (x + 1)^{2} : e^{x} x^{2} + 4 e^{x} x + 3 e^{x}

= e^{x} x^{2} + 4 e^{x} x + 3 e^{x}

x \to 9 lim (4 9 - x)

\frac{d}{d x} (ln (\frac{1}{x ^{3} + 3}))

4 y^{2} y d x + x y d y = 0

\frac{\partial}{\partial x} (ln (9 y e^{x y}))

d er i v a t i v e \frac{1}{3 x ^{3}}