derivative sqrt(x)(x-3)^2

Lösung

ableitung von

x (x - 3)^{2}

\frac{5 x ^{2} - 18 x + 9}{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

\frac{1}{2 x} (x - 3)^{2} + 2 (x - 3) x : \frac{5 x ^{2} - 18 x + 9}{2 x}

= \frac{5 x ^{2} - 18 x + 9}{2 x}

\frac{d}{d x} (3 x (sin (x) + cos (x)))

\frac{\partial}{\partial x} (x ln (z^{6} + x^{4}))

l a pl a ce t r an s f or m 2 \cdot e^{(5 \cdot t - 2)}

\int_{\frac{1}{7}}^{5} 10 x ln (7 x) d x

\frac{d}{d t} (1 - 3 t)