derivative x^3(x-6)^2

Lösung

ableitung von

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

5 x^{4} - 48 x^{3} + 108 x^{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{3}, g = (x - 6)^{2}

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

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

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

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

Vereinfache

3 x^{2} (x - 6)^{2} + 2 (x - 6) x^{3} : 5 x^{4} - 48 x^{3} + 108 x^{2}

= 5 x^{4} - 48 x^{3} + 108 x^{2}

\int x ln (x^{3}) d x

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

d er i v a t i v e (x - 3)^{- 2}

\frac{d y}{d x} = \frac{e ^{x}}{y ^{2}}

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