derivative y=(5x^4-3x^3)(3x^2-7x^3)

Lösung

ableitung von

y = (5 x^{4} - 3 x^{3}) (3 x^{2} - 7 x^{3})

- 245 x^{6} + 216 x^{5} - 45 x^{4}

Schritte zur Lösung

\frac{d}{d x} ((5 x^{4} - 3 x^{3}) (3 x^{2} - 7 x^{3}))

Wende die Produktregel an:

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

f = 5 x^{4} - 3 x^{3}, g = 3 x^{2} - 7 x^{3}

= \frac{d}{d x} (5 x^{4} - 3 x^{3}) (3 x^{2} - 7 x^{3}) + \frac{d}{d x} (3 x^{2} - 7 x^{3}) (5 x^{4} - 3 x^{3})

\frac{d}{d x} (5 x^{4} - 3 x^{3}) = 20 x^{3} - 9 x^{2}

\frac{d}{d x} (3 x^{2} - 7 x^{3}) = 6 x - 21 x^{2}

= (20 x^{3} - 9 x^{2}) (3 x^{2} - 7 x^{3}) + (6 x - 21 x^{2}) (5 x^{4} - 3 x^{3})

Vereinfache

(20 x^{3} - 9 x^{2}) (3 x^{2} - 7 x^{3}) + (6 x - 21 x^{2}) (5 x^{4} - 3 x^{3}) : - 245 x^{6} + 216 x^{5} - 45 x^{4}

= - 245 x^{6} + 216 x^{5} - 45 x^{4}

\int \frac{3 z ^{2}}{y} d y

t an g e n t - 5 x^{3} - 1

\int 2 cos (x) d x

y^{^{'}} + 5 y = 0

\frac{d}{d x} (x^{3} e^{\frac{1}{3} x} + \frac{2 x}{5 + x})