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

Lösung

ableitung von

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

135 x^{2} - 48 x - 28

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = (3 x - 2)^{2}, g = 5 x + 4

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

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

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

= 6 (3 x - 2) (5 x + 4) + 5 (3 x - 2)^{2}

Vereinfache

6 (3 x - 2) (5 x + 4) + 5 (3 x - 2)^{2} : 135 x^{2} - 48 x - 28

= 135 x^{2} - 48 x - 28

in v erse l a pl a ce \frac{- 1}{s ^{2} - 1}

\frac{d}{d x} (\frac{2}{x} + x)

\frac{\partial}{\partial v} (\frac{1}{u ^{2} + v ^{2}})

\int \frac{7 + 6 x}{1 + x ^{2}} d x

x \to 3 lim (2 x - 5)