is this right? $\displaystyle \frac{cos(x)}{(cos^4(x))^{\frac{3}{2}}} = cos^{-5}(x)$
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Looks good to me. Just a matter of using your power laws.
Looks good to me too.
Originally Posted by lllll I need some help simplifying: $\displaystyle \frac{cos(x)}{(cos^2(x))^{\frac{3}{2}}}$ Thanks in advance. $\displaystyle (\cos^2(x))^{3/2}=|cos(x)|^3$ so we get $\displaystyle \begin{cases} \sec^2(x) \mbox{if }-\frac{\pi}{2} < x < \frac{\pi}{2} \\ -\sec^2(x) \mbox{if } \frac{\pi}{2} < x < \frac{3\pi}{2} \end{cases}$
$\displaystyle (\cos^4(x))^{3/2}=|cos(x)|^6$ Dont forget that $\displaystyle \sqrt{x^2}=|x|$ example x=-2 Yours should be $\displaystyle \frac{1}{|\cos(x)|\cos^4(x)}$ try $\displaystyle x=\pi$
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