derivative of e^{4x}tan(x^5-4x^4)

Lösung

\frac{d}{d x} (e^{4 x} tan (x^{5} - 4 x^{4}))

e^{4 x} \cdot 4 tan (x^{5} - 4 x^{4}) + sec^{2} (x^{5} - 4 x^{4}) (5 x^{4} - 16 x^{3}) e^{4 x}

Schritte zur Lösung

\frac{d}{d x} (e^{4 x} tan (x^{5} - 4 x^{4}))

Wende die Produktregel an:

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

f = e^{4 x}, g = tan (x^{5} - 4 x^{4})

= \frac{d}{d x} (e^{4 x}) tan (x^{5} - 4 x^{4}) + \frac{d}{d x} (tan (x^{5} - 4 x^{4})) e^{4 x}

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

\frac{d}{d x} (tan (x^{5} - 4 x^{4})) = sec^{2} (x^{5} - 4 x^{4}) (5 x^{4} - 16 x^{3})

= e^{4 x} \cdot 4 tan (x^{5} - 4 x^{4}) + sec^{2} (x^{5} - 4 x^{4}) (5 x^{4} - 16 x^{3}) e^{4 x}

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