Derivatives

[Violagirl]

I'm reviewing for a Calc test and am stuck on this last problem.

If x tan theta=100 and dx/dt=8, find dTheta/dt when x=-2 and theta=pi/3.

 

[BigGlenntheHeavy]

$\displaystyle Given: \ xtan(\theta) \ = \ 100, \ \frac{dx}{dt} \ = \ 8$

$\displaystyle Find \ \frac{d \theta}{dt} \ when \ x \ = \ 2 \ and \ \theta \ = \ \frac{\pi}{3}.$

$\displaystyle \frac{dx}{dt}tan(\theta)+xsec^{2}(\theta)\frac{d \theta}{dt} \ = \ 0$

$\displaystyle 8tan(\frac{\pi}{3})+2sec^{2}(\frac{\pi}{3}) \frac{d \theta}{dt} \ = \ 0$

$\displaystyle 8\sqrt3+8\frac{d \theta}{dt} \ = \ 0$

$\displaystyle Hence, \ \frac{d \theta}{dt} \ = \ \frac{-8\sqrt3}{8} \ = \ -\sqrt3$