derivative f(x)=(2x+3)^{11}(4-5x)^9

Lösung

ableitung von

f (x) = (2 x + 3)^{11} (4 - 5 x)^{9}

22 (2 x + 3)^{10} (4 - 5 x)^{9} - 45 (4 - 5 x)^{8} (2 x + 3)^{11}

Schritte zur Lösung

\frac{d}{d x} ((2 x + 3)^{11} (4 - 5 x)^{9})

Wende die Produktregel an:

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

f = (2 x + 3)^{11}, g = (4 - 5 x)^{9}

= \frac{d}{d x} ((2 x + 3)^{11}) (4 - 5 x)^{9} + \frac{d}{d x} ((4 - 5 x)^{9}) (2 x + 3)^{11}

\frac{d}{d x} ((2 x + 3)^{11}) = 22 (2 x + 3)^{10}

\frac{d}{d x} ((4 - 5 x)^{9}) = - 45 (4 - 5 x)^{8}

= 22 (2 x + 3)^{10} (4 - 5 x)^{9} + (- 45 (4 - 5 x)^{8}) (2 x + 3)^{11}

Vereinfache

= 22 (2 x + 3)^{10} (4 - 5 x)^{9} - 45 (4 - 5 x)^{8} (2 x + 3)^{11}

x \to 1 + lim (1)

\frac{9}{10} x^{2} d y - 18 d x = 0

\frac{\partial}{\partial x} (x^{3} + x^{2} y - y^{2} - 4 y)

\frac{d}{d x} (4 x + 5)

x \to 5 + lim (\frac{2}{x + 5})