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Continue Learning about Calculus
What is derivative of cot t dt?
d/dt cot (t) dt = - cosec2(t)
If y equals x cube plus 2x and dx over dt equals 5 what is dy over dt when x equals 2?
y=x3+ 2x, dx/dt=5, x=2, dy/dt=? Differentiate the equation with respect to t. dy/dt=3x2*dx/dt Substitute in known values. dy/dt=3(2)2 * (5) dy/dt=60
Two cars start moving from the same point. One travels south at 60 mi per hour and the other travels west at 25 mi per hour. At what rate is the distance between the cars increasing two hours later?
dx/dt= 25 dy/dt=60 dz/dt=? x^ 2+y^2=z^2 2 x dx/dt +2 y dy/dt = 2 z dz/dt @ t = 2 x= 2* 25 = 50 y= 2* 60 =120 z=SQR (50^2 +120^2) = 130 2*50*25 +2* 120* 60 = 2* 130* dz/dt dz/dt = 65 mph .
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