Question

The equation \frac{t^2}{y^2} - \cos(6y) = -2 implicitly defines y as a function of t. Find \frac{dy}{dt}

          The equation \frac{t^2}{y^2} - \cos(6y) = -2 implicitly defines y as a function of t. Find \frac{dy}{dt}
        
The equation (t^2)/(y^2) - cos(6y) = -2 implicitly defines y as a function of t. Find (dy)/(dt)

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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The equation -(t^(2))/(y^(2))-cos(6y)=-2 implicitly defines y as a function of t. Find (dy)/(dt). (dy)/(dt)= The equation 2 cos (6 y) = 2 implicitly defines y as a function of dy Find at ain(a) A dy dt
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Transcript

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00:01 Hi, now given x as 4 secant t, y as 3 tan t, now we have to find d y by d x when t is equal to pi by 6 and write the equation of a tangent.
00:14 So first d x by d t will be equal to four second t tan t.
00:19 There a bit of second t is second t and d y by d t will be equal to three second square t so d y by d x will be equal to d .y by dt by dx by dt, which will be equal to three second square t by four secanty, tan, t.
00:38 So this will be equal to three by four second t by tan t, which is equal to three by four secant is one by cost t divided by sine t by cost t.
00:49 So we are left with three by four cossack t...
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