derivative y=4x^3sqrt(1-x^2)

Lösung

ableitung von

y = 4 x^{3} 1 - x^{2}

\frac{4 ( - 4 x ^{4} + 3 x ^{2} )}{1 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (4 x^{3} 1 - x^{2})

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{3} 1 - x^{2})

Wende die Produktregel an:

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

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

= 4 (\frac{d}{d x} (x^{3}) 1 - x^{2} + \frac{d}{d x} (1 - x^{2}) x^{3})

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

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

= 4 (3 x^{2} 1 - x^{2} + (- \frac{x}{1 - x ^{2}}) x^{3})

Vereinfache

4 (3 x^{2} 1 - x^{2} + (- \frac{x}{1 - x ^{2}}) x^{3}) : \frac{4 ( - 4 x ^{4} + 3 x ^{2} )}{1 - x ^{2}}

= \frac{4 ( - 4 x ^{4} + 3 x ^{2} )}{1 - x ^{2}}

\int \frac{x + 4}{x - 4} d x

\frac{d}{d t} (6 - 3 t^{2})

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

x \to - 1 lim (1 - 2 x)

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