derivative of (y(x^3e^{2x}+1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = y, g = x^{3} e^{2 x} + 1

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

\frac{d}{d x} (x^{3} e^{2 x} + 1) = 2 e^{2 x} x^{3} + 3 e^{2 x} x^{2}

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

\frac{d}{d y} ((z) (x^{2} e^{y} - y z e^{x}))

e x p an d \frac{( 2 x + 1 ) ( 2 x - 3 )}{2}

e x p an d \frac{y}{2 ( x + y )}

e x p an d (\frac{u - 1}{2})^{2}

e x p an d (x^{2} - x + 2) d x (x + 1) (x + 2) (x - 3)