derivative of (2-x^2(4x^2+9x)^4)

Lösung

\frac{d}{d x} ((2 - x^{2}) (4 x^{2} + 9 x)^{4})

- 2 x (4 x^{2} + 9 x)^{4} + 4 (4 x^{2} + 9 x)^{3} (8 x + 9) (2 - x^{2})

Schritte zur Lösung

\frac{d}{d x} ((2 - x^{2}) (4 x^{2} + 9 x)^{4})

Wende die Produktregel an:

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

f = 2 - x^{2}, g = (4 x^{2} + 9 x)^{4}

= \frac{d}{d x} (2 - x^{2}) (4 x^{2} + 9 x)^{4} + \frac{d}{d x} ((4 x^{2} + 9 x)^{4}) (2 - x^{2})

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

\frac{d}{d x} ((4 x^{2} + 9 x)^{4}) = 4 (4 x^{2} + 9 x)^{3} (8 x + 9)

= (- 2 x) (4 x^{2} + 9 x)^{4} + 4 (4 x^{2} + 9 x)^{3} (8 x + 9) (2 - x^{2})

Vereinfache

= - 2 x (4 x^{2} + 9 x)^{4} + 4 (4 x^{2} + 9 x)^{3} (8 x + 9) (2 - x^{2})

\frac{d}{d x} (\frac{5 ^{x}}{x ^{5}})

\int (x^{4} + x^{2} + x) d x

\frac{\partial}{\partial x} (x^{8})

t an g e n t y = \frac{1}{2 + 3 x}, (2, \frac{1}{8})

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