derivative of (2x^2+7(8x-4))

Lösung

\frac{d}{d x} ((2 x^{2} + 7) (8 x - 4))

48 x^{2} - 16 x + 56

Schritte zur Lösung

\frac{d}{d x} ((2 x^{2} + 7) (8 x - 4))

Wende die Produktregel an:

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

f = 2 x^{2} + 7, g = 8 x - 4

= \frac{d}{d x} (2 x^{2} + 7) (8 x - 4) + \frac{d}{d x} (8 x - 4) (2 x^{2} + 7)

\frac{d}{d x} (2 x^{2} + 7) = 4 x

\frac{d}{d x} (8 x - 4) = 8

= 4 x (8 x - 4) + 8 (2 x^{2} + 7)

Vereinfache

4 x (8 x - 4) + 8 (2 x^{2} + 7) : 48 x^{2} - 16 x + 56

= 48 x^{2} - 16 x + 56

\frac{d}{d x} (x^{- \frac{1}{2}} \cdot cos (x))

l a pl a ce t r an s f or m sin (\frac{2 t}{3})

\frac{d}{d x} (\frac{x}{( x - 7 ) ^{2}})

in v erse l a pl a ce \frac{6 s - 5}{s ^{2} + 7}

y^{^{'}} - \frac{2 y}{x} = x^{3} y^{- 3}