derivative of (2/5 ^{sqrt(x)})

Lösung

\frac{d}{d x} ((\frac{2}{5})^{x})

\frac{ln ( \frac{2}{5} ) \cdot 2 ^{x - 1}}{5 ^{x} x}

Schritte zur Lösung

\frac{d}{d x} ((\frac{2}{5})^{x})

Wende Exponentenregel an:

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

(\frac{2}{5})^{x} = e^{x l n (\frac{2}{5})}

= \frac{d}{d x} (e^{x l n (\frac{2}{5})})

Wende die Kettenregel an:

e^{x l n (\frac{2}{5})} \frac{d}{d x} (x ln (\frac{2}{5}))

= e^{x l n (\frac{2}{5})} \frac{d}{d x} (x ln (\frac{2}{5}))

\frac{d}{d x} (x ln (\frac{2}{5})) = \frac{ln ( \frac{2}{5} )}{2 x}

= e^{x l n (\frac{2}{5})} \frac{ln ( \frac{2}{5} )}{2 x}

Vereinfache

e^{x l n (\frac{2}{5})} \frac{ln ( \frac{2}{5} )}{2 x} : \frac{ln ( \frac{2}{5} ) \cdot 2 ^{x - 1}}{5 ^{x} x}

= \frac{ln ( \frac{2}{5} ) \cdot 2 ^{x - 1}}{5 ^{x} x}

\int (1 + x) (2 x + x^{2})^{5} d x

d er i v a t i v e f (x) = 3 t^{3} - 18 t^{2} + 2

x \to - \infty lim (- x)

\int 8 x (4 x^{2} + 4)^{4} d x

d er i v a t i v e \frac{2 x ^{4} + 5}{x ^{2}}