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

Lösung

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

\frac{5 x ^{2} - 6 x + 1}{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

= \frac{5 x ^{2} - 6 x + 1}{2 x}

\frac{\partial}{\partial x} (\frac{4 x}{5 + y})

d er i v a t i v e \frac{1}{c + k e ^{c}}

y^{^{''}} - 8 y^{^{'}} + 16 y = \frac{( 10.5 e ^{4 t} )}{( t ^{2} + 1 )}

d er i v a t i v e 55.6 - 22.1 v^{0.16}

(\frac{t ^{3}}{3})^{^{'}}