derivative (3x^2+1)(2x+2)^2

Lösung

ableitung von

(3 x^{2} + 1) (2 x + 2)^{2}

48 x^{3} + 72 x^{2} + 32 x + 8

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 3 x^{2} + 1, g = (2 x + 2)^{2}

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

\frac{d}{d x} (3 x^{2} + 1) = 6 x

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

= 6 x (2 x + 2)^{2} + 4 (2 x + 2) (3 x^{2} + 1)

Vereinfache

6 x (2 x + 2)^{2} + 4 (2 x + 2) (3 x^{2} + 1) : 48 x^{3} + 72 x^{2} + 32 x + 8

= 48 x^{3} + 72 x^{2} + 32 x + 8

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

\frac{\partial}{\partial x} (e^{x} + sin (y))

x \to 0 + lim (ln (sinh (x)))

\frac{d}{d x} (- 2 sin (x) - x)

f (x) = x + sin (x)