derivative of (6x^2+5(3x+sqrt(x)))

Lösung

\frac{d}{d x} ((6 x^{2} + 5) (3 x + x))

54 x^{2} + 12 x x + 3 x^{\frac{3}{2}} + \frac{5}{2 x} + 15

Schritte zur Lösung

\frac{d}{d x} ((6 x^{2} + 5) (3 x + x))

Wende die Produktregel an:

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

f = 6 x^{2} + 5, g = 3 x + x

= \frac{d}{d x} (6 x^{2} + 5) (3 x + x) + \frac{d}{d x} (3 x + x) (6 x^{2} + 5)

\frac{d}{d x} (6 x^{2} + 5) = 12 x

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

= 12 x (3 x + x) + (3 + \frac{1}{2 x}) (6 x^{2} + 5)

Vereinfache

12 x (3 x + x) + (3 + \frac{1}{2 x}) (6 x^{2} + 5) : 54 x^{2} + 12 x x + 3 x^{\frac{3}{2}} + \frac{5}{2 x} + 15

= 54 x^{2} + 12 x x + 3 x^{\frac{3}{2}} + \frac{5}{2 x} + 15

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

\frac{d ^{2} y}{d x ^{2}} = sin (2 x)

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

in v erse l a pl a ce \frac{1}{s + 4}

\frac{d}{d x} (\frac{4}{( x + 1 ) ^{2}})