derivative y=(x+5)(3sqrt(x)+8)

Lösung

ableitung von

y = (x + 5) (3 x + 8)

\frac{9 x + 15}{2 x} + 8

Schritte zur Lösung

\frac{d}{d x} ((x + 5) (3 x + 8))

Wende die Produktregel an:

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

f = x + 5, g = 3 x + 8

= \frac{d}{d x} (x + 5) (3 x + 8) + \frac{d}{d x} (3 x + 8) (x + 5)

\frac{d}{d x} (x + 5) = 1

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

= 1 \cdot (3 x + 8) + \frac{3}{2 x} (x + 5)

Vereinfache

1 \cdot (3 x + 8) + \frac{3}{2 x} (x + 5) : \frac{9 x + 15}{2 x} + 8

= \frac{9 x + 15}{2 x} + 8

\int \frac{( x + 1 )}{( x ^{2} + 2 x + 2 ) ^{3}} d x

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

d er i v a t i v e y = lo g_{4} (x) + lo g_{4} (x^{2})

\frac{d}{d x} (x^{2} - 8)

s l o p e (0, 2), (2, - 3)