derivative 2x^3sqrt(25-x^2)

Lösung

ableitung von

2 x^{3} 25 - x^{2}

\frac{2 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{3} 25 - x^{2})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (x^{3} 25 - x^{2})

Wende die Produktregel an:

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

f = x^{3}, g = 25 - x^{2}

= 2 (\frac{d}{d x} (x^{3}) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x^{3})

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

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 2 (3 x^{2} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{3})

Vereinfache

2 (3 x^{2} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{3}) : \frac{2 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

= \frac{2 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

x \to 0 + lim (1)

x \to 1 lim (\frac{e ^{x}}{x - 1})

\int 15 arctan (x) d x

d er i v a t i v e y = x (x - 10)

\frac{d}{d t} (\frac{2}{t ^{2} + 2})