derivative f(x)=sqrt(x)(x-6)^2

Lösung

ableitung von

f (x) = x (x - 6)^{2}

\frac{5 x ^{2} - 36 x + 36}{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

\frac{1}{2 x} (x - 6)^{2} + 2 (x - 6) x : \frac{5 x ^{2} - 36 x + 36}{2 x}

= \frac{5 x ^{2} - 36 x + 36}{2 x}

d er i v a t i v e 5 e^{x} + \frac{4}{3 x}

\frac{d}{d x} (2 sin (x) + 1)

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

\frac{d}{d x} (x^{4} sin (3 x))

d er i v a t i v e y = x sin (\frac{3}{x})