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

Lösung

ableitung von

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

48 x^{2} - 40 x + 12

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (4 x^{2} + 3) = 8 x

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

= 8 x (4 x - 5) + 4 (4 x^{2} + 3)

Vereinfache

8 x (4 x - 5) + 4 (4 x^{2} + 3) : 48 x^{2} - 40 x + 12

= 48 x^{2} - 40 x + 12

\frac{d}{d x} (ln (25))

x \to 0 lim (\frac{( 8 ^{x} - 1 )}{x})

\int \frac{d}{1} (x) d x

\int_{- 3}^{6} 3 + x d x

\frac{\partial}{\partial x} (e^{9 z})