derivative of (3x+1((x^2+4))/((6x-5)))

Lösung

\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

\frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

Wende die Produktregel an:

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

f = 3 x + 1, g = \frac{x ^{2} + 4}{6 x - 5}

= \frac{d}{d x} (3 x + 1) \frac{x ^{2} + 4}{6 x - 5} + \frac{d}{d x} (\frac{x ^{2} + 4}{6 x - 5}) (3 x + 1)

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

\frac{d}{d x} (\frac{x ^{2} + 4}{6 x - 5}) = \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}}

= 3 \cdot \frac{x ^{2} + 4}{6 x - 5} + \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}} (3 x + 1)

Vereinfache

3 \cdot \frac{x ^{2} + 4}{6 x - 5} + \frac{6 x ^{2} - 10 x - 24}{( 6 x - 5 ) ^{2}} (3 x + 1) : \frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

= \frac{36 x ^{3} - 39 x ^{2} - 10 x - 84}{( 6 x - 5 ) ^{2}}

\int \frac{sin ( 2 x )}{sin ( x )} d x

\frac{\partial}{\partial x} (\frac{1 - ln ( x )}{x ^{2}})

\frac{\partial}{\partial x} (ln (9 x))

t an g e n t y = x^{2} + 9 x, at x = - 8

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