derivative of (4x^3+3^2(5x^2+3))

Lösung

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

640 x^{7} + 288 x^{5} + 600 x^{4} + 216 x^{2} + 90 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = (4 x^{3} + 3)^{2}, g = 5 x^{2} + 3

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

\frac{d}{d x} ((4 x^{3} + 3)^{2}) = 24 x^{2} (4 x^{3} + 3)

\frac{d}{d x} (5 x^{2} + 3) = 10 x

= 24 x^{2} (4 x^{3} + 3) (5 x^{2} + 3) + 10 x (4 x^{3} + 3)^{2}

Vereinfache

24 x^{2} (4 x^{3} + 3) (5 x^{2} + 3) + 10 x (4 x^{3} + 3)^{2} : 640 x^{7} + 288 x^{5} + 600 x^{4} + 216 x^{2} + 90 x

= 640 x^{7} + 288 x^{5} + 600 x^{4} + 216 x^{2} + 90 x

y^{^{''}} + 6 y^{^{'}} + 34 y = 0, y (0) = 4, y^{^{'}} (0) = - 11

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

\int 55 - 6 x - x^{2} d x

d er i v a t i v e \frac{a x + b}{c x + d}

\frac{d}{d x} (2 x e^{2 x} + 2 x^{2} e^{2 x})