derivative f(x)=x^3(3-x)^2

Lösung

ableitung von

f (x) = x^{3} (3 - x)^{2}

5 x^{4} - 24 x^{3} + 27 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

3 x^{2} (3 - x)^{2} + (- 2 (3 - x)) x^{3} : 5 x^{4} - 24 x^{3} + 27 x^{2}

= 5 x^{4} - 24 x^{3} + 27 x^{2}

d er i v a t i v e y = cot^{2} (sin (x))

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

\int_{0}^{4} (3 t^{4} + 3 t + 2) d t

\frac{\partial}{\partial y} (2 x + 4 y)

d er i v a t i v e f (x) = 2 x - 1