derivative of e^{x^3}y

Lösung

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

e^{x^{3}} \cdot 3 x^{2} y + \frac{d y}{d x} e^{x^{3}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

= e^{x^{3}} \cdot 3 x^{2} y + \frac{d y}{d x} e^{x^{3}}

\int 10 x^{\frac{3}{2}} + 6 x - 8 d x

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

x \to 1 lim (\frac{- 3 x}{x - 1})

v^{'} = v^{2}

x \to 2 lim (2 x^{2})