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

Lösung

ableitung von

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

\frac{3 x ^{4} + 4 x ^{3} - 12 x ^{2}}{( x + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x - 2, g = \frac{1}{x + 2} x^{3}

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

\frac{d}{d x} (x - 2) = 1

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

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

Vereinfache

1 \cdot \frac{1}{x + 2} x^{3} + \frac{2 x ^{3} + 6 x ^{2}}{( x + 2 ) ^{2}} (x - 2) : \frac{3 x ^{4} + 4 x ^{3} - 12 x ^{2}}{( x + 2 ) ^{2}}

= \frac{3 x ^{4} + 4 x ^{3} - 12 x ^{2}}{( x + 2 ) ^{2}}

d er i v a t i v e y = (x + x^{2})^{\frac{1}{2}}

d er i v a t i v e lo g_{10} (sin (x^{2}))

d er i v a t i v e 5 sin (x + 1)

d er i v a t i v e \frac{l}{800}

d er i v a t i v e y = - 50