derivative 7sec^5(pit-8)

Lösung

ableitung von

7 sec^{5} (π t - 8)

35 π sec^{5} (π t - 8) tan (π t - 8)

Schritte zur Lösung

\frac{d}{d t} (7 sec^{5} (π t - 8))

Entferne die Konstante:

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

= 7 \frac{d}{d t} (sec^{5} (π t - 8))

Wende die Kettenregel an:

5 (sec (π t - 8))^{4} \frac{d}{d t} (sec (π t - 8))

= 5 (sec (π t - 8))^{4} \frac{d}{d t} (sec (π t - 8))

\frac{d}{d t} (sec (π t - 8)) = sec (π t - 8) tan (π t - 8) π

= 7 \cdot 5 (sec (π t - 8))^{4} sec (π t - 8) tan (π t - 8) π

Vereinfache

7 \cdot 5 sec^{4} (π t - 8) sec (π t - 8) tan (π t - 8) π : 35 π sec^{5} (π t - 8) tan (π t - 8)

= 35 π sec^{5} (π t - 8) tan (π t - 8)

x \to 4 lim (\frac{8 - 2 x}{x - 4})

\frac{d}{d x} (\frac{1}{( x - 4 ) ^{2}})

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

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