derivative g(x)=x^2(1-3x)

Lösung

ableitung von

g (x) = x^{2} (1 - 3 x)

2 x - 9 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x (1 - 3 x) + (- 3) x^{2} : 2 x - 9 x^{2}

= 2 x - 9 x^{2}

\int b x \cdot sin (\frac{π x}{2 a}) d x

\frac{\partial}{\partial y} (5 x^{2} - 2 x y + 3 y^{3})

s l o p e (5.8) (3.9)

y^{^{''}} - y = \frac{1}{e ^{x} + e ^{- x}}

\frac{\partial}{\partial x} (cos (x y))