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Answer 1 · 2017-11-12T18:42:09

$- 279 {(cos 9 x)}^{30} \cdot sin 9 x$ $-279(cos9x)^30*sin9x$

$y = {(cos 9 x)}^{31}$ $y=(cos9x)^31$

Take natural logarithm both sides,

$ln y = 31 \cdot ln (cos 9 x)$ $Lny=31*Ln(cos9x)$

Take derivative both sides,

$(y')/y=31*(-9sin9x)/(cos9x)$

$y'=(-279sin9x)/(cos9x)*y$

= $(-279sin9x)/(cos9x)*(cos9x)^31$

= $-279(cos9x)^30*sin9x$