Find dx/dt given x = sqrt(1 + cot 3t)?
dx/dt = 1/2 ( 1+cos3t) ^(-˝) [0 - cosec˛ 3t(3)]
dx/dt = 1/2{ 1/(1+cost3t)˝ } {-3cosec˛ 3t}
= [ (-3/2 ) (cosec˛3t) {1/(1+cos3t)˝} ]
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Find $\displaystyle \frac{dx}{dt}$ given $\displaystyle x = \sqrt{1 + cot 3t}$?
$\displaystyle \frac{dx}{dt} = \frac{1}{2}( 1+cot(3t))^{\frac{-1}{2}}[0 - csc˛(3t)]$
$\displaystyle \frac{dx}{dt} = \frac{1}{2}\frac{1}{\sqrt{1+cot(3t)}}{(-3csc˛ (3t))}$
= $\displaystyle (\frac{-3}{2}) (csc˛(3t)) {\frac{1}{\sqrt{1+cot(3t)}}$
=$\displaystyle \frac{-3csc^{2}(3t)}{2\sqrt{1+cot(3t)}}$