derivative of ({f}(x(x)^2)(x^3-2x^2-6))

Lösung

\frac{d}{d x} ((f (x) (x)^{2}) (x^{3} - 2 x^{2} - 6))

\frac{d}{d x} (f (x)) x^{2} (x^{3} - 2 x^{2} - 6) + (5 x^{4} - 8 x^{3} - 12 x) f (x)

Schritte zur Lösung

\frac{d}{d x} ((f (x) (x)^{2}) (x^{3} - 2 x^{2} - 6))

Wende die Produktregel an:

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

f = f (x), g = x^{2} (x^{3} - 2 x^{2} - 6)

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

\frac{d}{d x} (x^{2} (x^{3} - 2 x^{2} - 6)) = 5 x^{4} - 8 x^{3} - 12 x

= \frac{d}{d x} (f (x)) x^{2} (x^{3} - 2 x^{2} - 6) + (5 x^{4} - 8 x^{3} - 12 x) f (x)

e x p an d d x (\frac{e ^{- \frac{2 x}{L}} w ^{3}}{6} + Cw + C)

e x p an d \frac{5 x - 2}{( 5 x + 4 ) ^{2}}

e x p an d \frac{4}{s ^{2} ( s ^{2} - 4 )}

e x p an d \frac{1 - 2 t}{t ^{2} ( 1 - t ) ^{2}}

s im pl i f y x (x^{2} - x + \frac{1}{6}) (x - \frac{1}{2})