derivative g(x)=x^2(1-5x)

Lösung

ableitung von

g (x) = x^{2} (1 - 5 x)

2 x - 15 x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} (1 - 5 x))

Wende die Produktregel an:

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

f = x^{2}, g = 1 - 5 x

= \frac{d}{d x} (x^{2}) (1 - 5 x) + \frac{d}{d x} (1 - 5 x) x^{2}

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

\frac{d}{d x} (1 - 5 x) = - 5

= 2 x (1 - 5 x) + (- 5) x^{2}

Vereinfache

2 x (1 - 5 x) + (- 5) x^{2} : 2 x - 15 x^{2}

= 2 x - 15 x^{2}

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

x \to - 8 + lim (\frac{x}{x + 8})

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

\int_{1}^{R} x^{- \frac{7}{5}} d x

\frac{d}{d x} ((6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1))