derivative of (3x^2+4^2(4x^2-8)^2)

Lösung

\frac{d}{d x} ((3 x^{2} + 4)^{2} (4 x^{2} - 8)^{2})

1152 x^{7} - 1152 x^{5} - 2816 x^{3} + 1024 x

Schritte zur Lösung

\frac{d}{d x} ((3 x^{2} + 4)^{2} (4 x^{2} - 8)^{2})

Wende die Produktregel an:

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

f = (3 x^{2} + 4)^{2}, g = (4 x^{2} - 8)^{2}

= \frac{d}{d x} ((3 x^{2} + 4)^{2}) (4 x^{2} - 8)^{2} + \frac{d}{d x} ((4 x^{2} - 8)^{2}) (3 x^{2} + 4)^{2}

\frac{d}{d x} ((3 x^{2} + 4)^{2}) = 12 x (3 x^{2} + 4)

\frac{d}{d x} ((4 x^{2} - 8)^{2}) = 16 x (4 x^{2} - 8)

= 12 x (3 x^{2} + 4) (4 x^{2} - 8)^{2} + 16 x (4 x^{2} - 8) (3 x^{2} + 4)^{2}

Vereinfache

12 x (3 x^{2} + 4) (4 x^{2} - 8)^{2} + 16 x (4 x^{2} - 8) (3 x^{2} + 4)^{2} : 1152 x^{7} - 1152 x^{5} - 2816 x^{3} + 1024 x

= 1152 x^{7} - 1152 x^{5} - 2816 x^{3} + 1024 x

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (1) = 0, y^{^{'}} (1) = 1

d er i v a t i v e (x^{4} + 3 x^{2} - 2)^{5}

(x + 1) y^{^{'}} + (x + 2) y = 8 x e^{- x}

\int 8 x^{3} e^{x^{4}} d x

d er i v a t i v e 8 x sin (x)