Answer
a) $2xsin(9-x^2)$
b)$x^{-2}sin(x^{-1})$
c)$-sec^2xsin(tanx)$
Work Step by Step
a) $u(x) = 9-x^2$
$\frac{d}{dx}cos(9-x^2)$
$=u'(x)cos'(9-x^2)$
$=(-2x)(-sin(9-x^2))$
$=2xsin(9-x^2)$
b) $u(x) = x^{-1}$
$\frac{d}{dx}cos(x^{-1})$
$=u'(x)cos'(x^{-1})$
$=(-x^{-2})(-sin(x^{-1}))$
$=x^{-2}sin(x^{-1})$
c) $u(x) = tanx$
$\frac{d}{dx}cos(tanx)$
$=u'(x)cos'(tanx)$
$=sec^2x(-sin(tanx))$
$=-sec^2xsin(tanx)$
