derivative of sec^9(2^x)

Lösung

\frac{d}{d x} (sec^{9} (2^{x}))

9 ln (2) \cdot 2^{x} sec^{9} (2^{x}) tan (2^{x})

Schritte zur Lösung

\frac{d}{d x} (sec^{9} (2^{x}))

Wende die Kettenregel an:

9 (sec (2^{x}))^{8} \frac{d}{d x} (sec (2^{x}))

= 9 (sec (2^{x}))^{8} \frac{d}{d x} (sec (2^{x}))

\frac{d}{d x} (sec (2^{x})) = sec (2^{x}) tan (2^{x}) \cdot 2^{x} ln (2)

= 9 (sec (2^{x}))^{8} sec (2^{x}) tan (2^{x}) \cdot 2^{x} ln (2)

Vereinfache

9 sec^{8} (2^{x}) sec (2^{x}) tan (2^{x}) \cdot 2^{x} ln (2) : 9 ln (2) \cdot 2^{x} sec^{9} (2^{x}) tan (2^{x})

= 9 ln (2) \cdot 2^{x} sec^{9} (2^{x}) tan (2^{x})

\int 7 ln (3 x) d x

\frac{d}{d x} (x \cdot e^{x} + e^{x})

d er i v a t i v e f (x) = e^{x^{3} l n (x)}

d er i v a t i v e f (x) = \frac{6}{3 x + 1}

d er i v a t i v e f (x) = 8 - 2 x