derivative f(x)=5xsqrt(1-x^3)

Lösung

ableitung von

f (x) = 5 x 1 - x^{3}

\frac{5 ( - 5 x ^{3} + 2 )}{2 1 - x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (5 x 1 - x^{3})

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x 1 - x^{3})

Wende die Produktregel an:

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

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

= 5 (\frac{d x}{d x} 1 - x^{3} + \frac{d}{d x} (1 - x^{3}) x)

\frac{d x}{d x} = 1

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

= 5 (1 \cdot 1 - x^{3} + (- \frac{3 x ^{2}}{2 1 - x ^{3}}) x)

Vereinfache

5 (1 \cdot 1 - x^{3} + (- \frac{3 x ^{2}}{2 1 - x ^{3}}) x) : \frac{5 ( - 5 x ^{3} + 2 )}{2 1 - x ^{3}}

= \frac{5 ( - 5 x ^{3} + 2 )}{2 1 - x ^{3}}

\frac{d}{d x} (\frac{7 x + 8}{4 x + 8})

\int 1. 8^{(0.045 x)} - 1 d x

\int - x^{2} e^{- x} d x

(1 - x^{2}) y^{^{''}} - 2 x y^{^{'}} = 1

x \to 0 lim (1 - 1 - x)