derivative y=9x^2e^x

Lösung

ableitung von

y = 9 x^{2} e^{x}

9 (2 x e^{x} + e^{x} x^{2})

Schritte zur Lösung

\frac{d}{d x} (9 x^{2} e^{x})

Entferne die Konstante:

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

= 9 \frac{d}{d x} (x^{2} e^{x})

Wende die Produktregel an:

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

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

= 9 (\frac{d}{d x} (x^{2}) e^{x} + \frac{d}{d x} (e^{x}) x^{2})

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

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

= 9 (2 x e^{x} + e^{x} x^{2})

n = 1 \sum \infty (- 5)^{- n}

\frac{d}{d x} (sin^{2} (x) + 2^{s i n (x)})

n = 1 \sum \infty \frac{n}{n ^{2} + 1}

\frac{d}{d x} (x^{\frac{1}{3}} y^{\frac{2}{3}})

\frac{d}{d x} (\frac{1}{2} x^{2} - x + \frac{1}{6} x^{3})