derivative of 3^{x-2}

Lösung

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

ln (3) \cdot 3^{x - 2}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

3^{x - 2} = e^{(x - 2) l n (3)}

= \frac{d}{d x} (e^{(x - 2) l n (3)})

Wende die Kettenregel an:

e^{(x - 2) l n (3)} \frac{d}{d x} ((x - 2) ln (3))

= e^{(x - 2) l n (3)} \frac{d}{d x} ((x - 2) ln (3))

\frac{d}{d x} ((x - 2) ln (3)) = ln (3)

= e^{(x - 2) l n (3)} ln (3)

e^{(x - 2) l n (3)} = 3^{x - 2}

= ln (3) \cdot 3^{x - 2}

t an g e n t f (x) = 4 - x, at x = 0

\frac{\partial}{\partial v} (u + v)

d er i v a t i v e \frac{x}{x ^{2} 1}

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

t an g e n t f (x) = \frac{7}{x + 1}, at x = 7