derivative of (x+6(x-2)^2)

Lösung

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

3 x^{2} + 4 x - 20

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= 3 x^{2} + 4 x - 20

\frac{\partial}{\partial x} (x^{2} y - y^{2} x)

d er i v a t i v e e^{(x - 1)^{2}}

d er i v a t i v e y = (\frac{8 x ^{2} - 5}{2 - x})^{3}

d er i v a t i v e g (x) = lo g_{7} (8 x^{3} - 9 x^{2})

\int x (x sin (x) - cos (x)) d x