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

Lösung

ableitung von

f (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}

\int \frac{30}{( 225 x ^{2} + 1 ) ^{2}} d x

d er i v a t i v e \frac{10}{( 1 + e ^{- x} )}

\frac{\partial}{\partial x} (e^{\frac{2}{x}})

\int_{3}^{\infty} 1

\int (2 x - 7)^{5} d x