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Beliebt Rechnen >

derivative of (x^3+6e^x)

Lösung

\frac{d}{d x} ((x^{3} + 6) e^{x})

Lösung

3 x^{2} e^{x} + e^{x} (x^{3} + 6)

Schritte zur Lösung

\frac{d}{d x} ((x^{3} + 6) e^{x})

Wende die Produktregel an:

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

f = x^{3} + 6, g = e^{x}

= \frac{d}{d x} (x^{3} + 6) e^{x} + \frac{d}{d x} (e^{x}) (x^{3} + 6)

\frac{d}{d x} (x^{3} + 6) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} (x^{3} + 6)

Graph

Beliebte Beispiele

derivative of sinh(0)

\frac{d}{d x} (sinh (0))

(dv)/(dt)= 1/(t^2)

\frac{d v}{d t} = \frac{1}{t ^{2}}

tangent 3-2cos(x),\at x= pi/2

t an g e n t 3 - 2 cos (x), at x = \frac{π}{2}

integral of 8/(8+e^x)

\int \frac{8}{8 + e ^{x}} d x

steigung y^2=9x,\at x=16

s l o p e y^{2} = 9 x, at x = 16