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Beliebt Rechnen >

d/(dy)(e^{3x}(3x^2y+2xy+y^3))

Lösung

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

Lösung

e^{3 x} (3 x^{2} + 2 x + 3 y^{2})

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

= e^{3 x} (3 x^{2} + 2 x + 3 y^{2})

Beliebte Beispiele

integral of (cos(3t)+3)/(sin(3t))

\int \frac{cos ( 3 t ) + 3}{sin ( 3 t )} d t

integral of (2ln(x))/(x^3)

\int \frac{2 ln ( x )}{x ^{3}} d x

integral of 2x+6

\int 2 x + 6 d x

inverselaplace 1/(s^4(s+3))

in v erse l a pl a ce \frac{1}{s ^{4} ( s + 3 )}

(\partial)/(\partial z)(z/(x^2+y^2+z^2))

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