erweitern (e^{4x})(x^2(dy)/(dx)+2xy)

Lösung

erweitern

(e^{4 x}) (x^{2} \frac{d y}{d x} + 2 x y)

e^{4 x} x^{2} \frac{d y}{d x} + 2 e^{4 x} x y

Schritte zur Lösung

(e^{4 x}) (x^{2} \frac{d y}{d x} + 2 x y)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = (e^{4 x}), b = x^{2} \frac{d y}{d x}, c = 2 x y

= (e^{4 x}) x^{2} \frac{d y}{d x} + (e^{4 x}) \cdot 2 x y

= x^{2} (e^{4 x}) \frac{d y}{d x} + 2 x y (e^{4 x})

Entferne die Klammern:

(a) = a

= e^{4 x} x^{2} \frac{d y}{d x} + 2 e^{4 x} x y

e x p an d \frac{1}{( A \cdot x ^{2} + 1 ) \cdot x ^{2}}

\frac{d}{d t} ((a (t)) (a (t)^{4} + t^{4} - 6 a (t)^{2} t))

e x p an d \frac{j + 2}{( - 2 + j ) ( j - 1 ) ( j ^{2} + 2 j + 5 )}

e x p an d (3^{^{'}} x^{2^{^{'}}} - 6 x + 4) (- 2 x^{2} + 7 x + 5)^{^{'}}

e x p an d \frac{( 3 + 9 x )}{( 1 + x ) ( 3 + 5 x )}