derivative of 8(0.9^{x-2})

Lösung

\frac{d}{d x} (8 (0.9)^{x - 2})

- 0.84288 \dots \cdot 0. 9^{x - 2}

Schritte zur Lösung

\frac{d}{d x} (8 (0.9)^{x - 2})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (0. 9^{x - 2})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

0. 9^{x - 2} = e^{(x - 2) l n (0.9)}

= 8 \frac{d}{d x} (e^{(x - 2) l n (0.9)})

Wende die Kettenregel an:

e^{(x - 2) l n (0.9)} \frac{d}{d x} ((x - 2) ln (0.9))

= e^{(x - 2) l n (0.9)} \frac{d}{d x} ((x - 2) ln (0.9))

\frac{d}{d x} ((x - 2) ln (0.9)) = - 0.10536 \dots

= 8 e^{(x - 2) l n (0.9)} (- 0.10536 \dots)

Vereinfache

8 e^{(x - 2) l n (0.9)} (- 0.10536 \dots) : - 0.84288 \dots \cdot 0. 9^{x - 2}

= - 0.84288 \dots \cdot 0. 9^{x - 2}

x y^{^{'}} = y^{2} - y, y (2) = 1

\int_{0}^{1} \frac{1}{( x ^{2} + 1 ) ^{3}} d x

t an g e n t f (x) = 3 x^{2} - 5 x + 8, at x = 2

in v erse l a pl a ce \frac{2}{( s ^{2} - 1 ) ( s - 1 )}

\frac{\partial}{\partial y} (x^{2} + 5 y^{2})