derivative of xsqrt(x+6)

Lösung

\frac{d}{d x} (x x + 6)

\frac{3 x + 12}{2 x + 6}

Schritte zur Lösung

\frac{d}{d x} (x x + 6)

Wende die Produktregel an:

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

f = x, g = x + 6

= \frac{d x}{d x} x + 6 + \frac{d}{d x} (x + 6) x

\frac{d x}{d x} = 1

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

= 1 \cdot x + 6 + \frac{1}{2 x + 6} x

Vereinfache

1 \cdot x + 6 + \frac{1}{2 x + 6} x : \frac{3 x + 12}{2 x + 6}

= \frac{3 x + 12}{2 x + 6}

x \to \infty lim (- \frac{1}{x} + 1)

d er i v a t i v e f (x) = ln (\frac{4 + x ^{2}}{x})

t an g e n t f (x) = 20 x, (4, 40)

y^{^{''}} + 5 y^{^{'}} - 2 y = 0

\int \frac{1}{t ^{2} - 12 t + 40} d t