derivative (3x-1)^2(x^2+1)^2

Lösung

ableitung von

(3 x - 1)^{2} (x^{2} + 1)^{2}

54 x^{5} - 30 x^{4} + 76 x^{3} - 36 x^{2} + 22 x - 6

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = (3 x - 1)^{2}, g = (x^{2} + 1)^{2}

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

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

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

= 6 (3 x - 1) (x^{2} + 1)^{2} + 4 x (x^{2} + 1) (3 x - 1)^{2}

Vereinfache

6 (3 x - 1) (x^{2} + 1)^{2} + 4 x (x^{2} + 1) (3 x - 1)^{2} : 54 x^{5} - 30 x^{4} + 76 x^{3} - 36 x^{2} + 22 x - 6

= 54 x^{5} - 30 x^{4} + 76 x^{3} - 36 x^{2} + 22 x - 6

y^{^{'}} - y = 9 t

\int sec^{6} (3 y) tan^{2} (3 y) d y

\frac{\partial}{\partial x} ((2 x) (3 z))

\frac{d y}{d x} = 6 y

\int (cos (x))^{2} - (sin (x))^{2} d x