derivative of x^3e^{x^2}

Lösung

\frac{d}{d x} (x^{3} e^{x^{2}})

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

Schritte zur Lösung

\frac{d}{d x} (x^{3} e^{x^{2}})

Wende die Produktregel an:

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

f = x^{3}, g = e^{x^{2}}

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} e^{x^{2}} + e^{x^{2}} \cdot 2 x x^{3}

e^{x^{2}} \cdot 2 x x^{3} = 2 e^{x^{2}} x^{4}

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

d er i v a t i v e f (x) = (3 x - 2)^{4}

\int cos (2 x) - 1 d x

\frac{d y}{d x} = \frac{( x - y )}{( x + 2 y )}

\frac{\partial}{\partial x} (x^{2} + z^{2})

\frac{d}{d x} (\frac{3 x ^{2} + 2 x}{4 x - 3})