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Beliebt Rechnen >

derivative of (x^3+4e^{3x})

Lösung

\frac{d}{d x} ((x^{3} + 4) e^{3 x})

Lösung

3 x^{2} e^{3 x} + e^{3 x} \cdot 3 (x^{3} + 4)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 4) e^{3 x})

Wende die Produktregel an:

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

f = x^{3} + 4, g = e^{3 x}

= \frac{d}{d x} (x^{3} + 4) e^{3 x} + \frac{d}{d x} (e^{3 x}) (x^{3} + 4)

\frac{d}{d x} (x^{3} + 4) = 3 x^{2}

\frac{d}{d x} (e^{3 x}) = e^{3 x} \cdot 3

= 3 x^{2} e^{3 x} + e^{3 x} \cdot 3 (x^{3} + 4)

Graph

Beliebte Beispiele

integral of (ln(-2x))/(5x)

\int \frac{ln ( - 2 x )}{5 x} d x

fläche y=x^2-7,y=6x

a re a y = x^{2} - 7, y = 6 x

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

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

tangent f(x)= 1/(x-1),\at x=-4

t an g e n t f (x) = \frac{1}{x - 1}, at x = - 4

derivative of e^{x^3+5x}

\frac{d}{d x} (e^{x^{3} + 5 x})