derivative of (sqrt(x)-2(3sqrt(x)+8))

Lösung

\frac{d}{d x} ((x - 2) (3 x + 8))

\frac{3 x + 1}{x}

Schritte zur Lösung

\frac{d}{d x} ((x - 2) (3 x + 8))

Wende die Produktregel an:

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

f = x - 2, g = 3 x + 8

= \frac{d}{d x} (x - 2) (3 x + 8) + \frac{d}{d x} (3 x + 8) (x - 2)

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

\frac{d}{d x} (3 x + 8) = \frac{3}{2 x}

= \frac{1}{2 x} (3 x + 8) + \frac{3}{2 x} (x - 2)

Vereinfache

\frac{1}{2 x} (3 x + 8) + \frac{3}{2 x} (x - 2) : \frac{3 x + 1}{x}

= \frac{3 x + 1}{x}

\int \frac{x + 2}{5 x + 6} d x

\frac{d}{d x} (e^{x} cos (x) - sin (x) e^{x})

y^{^{''}} + 36 y^{^{'}} = 0

x \to \frac{π}{2} + lim (sec (x))

\int x (9 - x^{2}) d x