derivative y=(5x-4)^5(3-x^3)^5

Lösung

ableitung von

y = (5 x - 4)^{5} (3 - x^{3})^{5}

25 (5 x - 4)^{4} (3 - x^{3})^{5} - 15 x^{2} (3 - x^{3})^{4} (5 x - 4)^{5}

Schritte zur Lösung

\frac{d}{d x} ((5 x - 4)^{5} (3 - x^{3})^{5})

Wende die Produktregel an:

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

f = (5 x - 4)^{5}, g = (3 - x^{3})^{5}

= \frac{d}{d x} ((5 x - 4)^{5}) (3 - x^{3})^{5} + \frac{d}{d x} ((3 - x^{3})^{5}) (5 x - 4)^{5}

\frac{d}{d x} ((5 x - 4)^{5}) = 25 (5 x - 4)^{4}

\frac{d}{d x} ((3 - x^{3})^{5}) = - 15 x^{2} (3 - x^{3})^{4}

= 25 (5 x - 4)^{4} (3 - x^{3})^{5} + (- 15 x^{2} (3 - x^{3})^{4}) (5 x - 4)^{5}

Vereinfache

= 25 (5 x - 4)^{4} (3 - x^{3})^{5} - 15 x^{2} (3 - x^{3})^{4} (5 x - 4)^{5}