Question

find f'(x)
f(x)=1/(secx)^7

Answer 1

\[\Large\bf\sf \sec x\quad=\quad \frac{1}{\cos x}\]
Use that^\[\Large\bf\sf \left(\frac{1}{\sec x}\right)^7\quad=\quad ?\]

Answer 2

\[\frac{ 1 }{ (secx)^7 }\]

Answer 3

??

Answer 4

Use the identity.

Answer 5

\[\Large\bf\sf \sec x\quad=\quad \frac{1}{\cos x}\qquad\implies\qquad \frac{1}{\sec x}\quad=\quad \cos x\]

Answer 6

\[\Large\bf\sf \left(\frac{1}{\sec x}\right)^7\quad=\quad ?\]

Answer 7

so it wont be secx=secxtanx

Answer 8

cos (x)

Answer 9

\[\Large\bf\sf \left(\frac{1}{\sec x}\right)^7\quad=\quad (\cos x)^7\]

Answer 10

Going off of what zepdrix said, you then use the Chain-Chain Rule to find f'(x) = 7(cosx) * - sinx => f'(x) = -7sinxcosx.

Answer 11

*7(cosx)^6 * -sinx => f'(x) = -7(sinx)(cosx)^6