derivative f(x)=(2x-3)(x+3)^3

Lösung

ableitung von

f (x) = (2 x - 3) (x + 3)^{3}

2 (x + 3)^{3} + 3 (x + 3)^{2} (2 x - 3)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 2 (x + 3)^{3} + 3 (x + 3)^{2} (2 x - 3)

\int \frac{x ^{- 1} - x ^{- 3} + x ^{- 3}}{x ^{2}} d x

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

f (x) = e^{x^{4}}

6 x \frac{d y}{d x} = 2 x e^{x} - 6 y + 6 x^{2}

\frac{\partial}{\partial x} (ln (x + 2))