derivative x^3e^{6x^3+8x^2-7}

Lösung

ableitung von

x^{3} e^{6 x^{3} + 8 x^{2} - 7}

3 x^{2} e^{6 x^{3} + 8 x^{2} - 7} + e^{6 x^{3} + 8 x^{2} - 7} (18 x^{2} + 16 x) x^{3}

Schritte zur Lösung

\frac{d}{d x} (x^{3} e^{6 x^{3} + 8 x^{2} - 7})

Wende die Produktregel an:

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

f = x^{3}, g = e^{6 x^{3} + 8 x^{2} - 7}

= \frac{d}{d x} (x^{3}) e^{6 x^{3} + 8 x^{2} - 7} + \frac{d}{d x} (e^{6 x^{3} + 8 x^{2} - 7}) x^{3}

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

\frac{d}{d x} (e^{6 x^{3} + 8 x^{2} - 7}) = e^{6 x^{3} + 8 x^{2} - 7} (18 x^{2} + 16 x)

= 3 x^{2} e^{6 x^{3} + 8 x^{2} - 7} + e^{6 x^{3} + 8 x^{2} - 7} (18 x^{2} + 16 x) x^{3}

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