derivative of (x-3xsqrt(x)/(sqrt(x)))

Lösung

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

\frac{1 - 3 x}{2 x} - \frac{3}{2}

Schritte zur Lösung

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

Vereinfache

\frac{x - 3 x x}{x} : x (1 - 3 x)

= \frac{d}{d x} (x (1 - 3 x))

Wende die Produktregel an:

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

f = x, g = 1 - 3 x

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

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

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

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

Vereinfache

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

= \frac{1 - 3 x}{2 x} - \frac{3}{2}

d er i v a t i v e \frac{4 + x ^{2}}{4 - x}

t an g e n t f (x) = (12 x - 8)^{\frac{1}{2}}, at x = 2

\frac{d y}{d x} = 7 x y^{2}

\frac{\partial}{\partial x} (3 x^{2} y + 2 y)

\int_{1}^{2} x e^{x} d x