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Beliebt Algebra >

d/(dw)((z)(e^{zw}))

Lösung

\frac{d}{d w} ((z (w)) (e^{z (w) w}))

Lösung

\frac{d z}{d w} e^{z w} + e^{z w} (w \frac{d z}{d w} + z) z

Schritte zur Lösung

\frac{d}{d w} ((z) (e^{z w}))

Wende die Produktregel an:

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

f = z, g = e^{z w}

= \frac{d z}{d w} e^{z w} + \frac{d}{d w} (e^{z w}) z

\frac{d}{d w} (e^{z w}) = e^{z w} (w \frac{d z}{d w} + z)

= \frac{d z}{d w} e^{z w} + e^{z w} (w \frac{d z}{d w} + z) z

Beliebte Beispiele

f(x)=(sin(3x))^4

f (x) = (sin (3 x))^{4}

f(x)=12(cos(2000pix))^2

f (x) = 12 (cos (2000 π x))^{2}

faktorisieren ax^2-a+bx^2-b

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faktorisieren (4x^4)(4x^4)

f a c t or (4 x^{4}) (4 x^{4})

faktorisieren (x^2-1)^2+(2x)^2

f a c t or (x^{2} - 1)^{2} + (2 x)^{2}