derivative of (3x^2-x-4(-x^2+2))

Lösung

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

- 12 x^{3} + 3 x^{2} + 20 x - 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (3 x^{2} - x - 4) = 6 x - 1

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

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

Vereinfache

(6 x - 1) (- x^{2} + 2) + (- 2 x) (3 x^{2} - x - 4) : - 12 x^{3} + 3 x^{2} + 20 x - 2

= - 12 x^{3} + 3 x^{2} + 20 x - 2

h \to 0.001 lim (\frac{e ^{h} - 1}{h})

\int \frac{x ^{3}}{( 1 - 16 x ^{2} ) ^{\frac{3}{2}}} d x

x \to 0 lim (10 x)

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

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