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Beliebt Rechnen >

derivative 7z^2e^z

Lösung

ableitung von

7 z^{2} e^{z}

Lösung

7 (2 z e^{z} + e^{z} z^{2})

Schritte zur Lösung

\frac{d}{d z} (7 z^{2} e^{z})

Entferne die Konstante:

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

= 7 \frac{d}{d z} (z^{2} e^{z})

Wende die Produktregel an:

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

f = z^{2}, g = e^{z}

= 7 (\frac{d}{d z} (z^{2}) e^{z} + \frac{d}{d z} (e^{z}) z^{2})

\frac{d}{d z} (z^{2}) = 2 z

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

= 7 (2 z e^{z} + e^{z} z^{2})

Graph

Beliebte Beispiele

integral of (x+1)/(sqrt(x^2+2x+3))

\int \frac{x + 1}{x ^{2} + 2 x + 3} d x

(7x+5y)dx+(5x-8y3)dy=0

(7 x + 5 y) d x + (5 x - 8 y 3) d y = 0

tangent f(x)=x^4,\at x=3

t an g e n t f (x) = x^{4}, at x = 3

integral of sqrt(1+(x/2-4)^2)

\int 1 + (\frac{x}{2} - 4)^{2} d x

integral of 3+2cos(x)

\int 3 + 2 cos (x) d x