derivative of 5^{mx}

Lösung

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

ln (5) \cdot 5^{m x} m

Schritte zur Lösung

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

Wende Exponentenregel an:

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

5^{m x} = e^{m x l n (5)}

= \frac{d}{d x} (e^{m x l n (5)})

Wende die Kettenregel an:

e^{m x l n (5)} \frac{d}{d x} (m x ln (5))

= e^{m x l n (5)} \frac{d}{d x} (m x ln (5))

\frac{d}{d x} (m x ln (5)) = ln (5) m

= e^{m x l n (5)} ln (5) m

e^{m x l n (5)} = 5^{m x}

= ln (5) \cdot 5^{m x} m

x \to 0 - lim (e^{x})

\int_{0}^{2 π} cos (t) sin (t) d t

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

x \to - \frac{1}{2} lim (\frac{( 6 x - 1 )}{x})