derivative of x^2(1-x^2^3)

Lösung

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

2 x (1 - x^{2})^{3} - 6 x^{3} (1 - x^{2})^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((1 - x^{2})^{3}) = - 6 x (1 - x^{2})^{2}

= 2 x (1 - x^{2})^{3} + (- 6 x (1 - x^{2})^{2}) x^{2}

Vereinfache

2 x (1 - x^{2})^{3} + (- 6 x (1 - x^{2})^{2}) x^{2} : 2 x (1 - x^{2})^{3} - 6 x^{3} (1 - x^{2})^{2}

= 2 x (1 - x^{2})^{3} - 6 x^{3} (1 - x^{2})^{2}

\frac{d}{d x} (e^{3 x - 2 y} + x^{2} e^{- 2 y})

t a y l or \frac{x}{2 + x ^{2}}

\int 2 (3 x - 4) d x

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

\frac{d}{d x} (x^{x} + 2^{x} ln (x))