We are given the following parametric equations and asked to find derivatives with respect to t and also dx x = 8t3 + 6t y = 9t – 7t2 Recall that x and y are simply functions of t, so we find their derivatives with respect to t as usual. dx dt dy dt

Q: 2. Answer the following derivative related questions. dy. (1) Let y = x' + 4x³ + 2x² + 16, find ; dx…

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Q: Determine the second derivative of the parametrically defined curve represented by the equations…

A: dsintdt=costdcostdt=-sintdydx=dydtdxdt

Q: dy given the equation 2² + y° = e". Use implicit differentiation to determine dr dy da ||

A: The equation is given by x2 + y5 = ey To evaluate : dydx

Q: x = tan t The parametric equations represent a curve. ly= cos t A. Write this as a vector-valued…

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Q: Ex 1. Calculate the derivative i) x² + y² = 1. dy 33 dx for the following: ii) xy= x²+y.

A: To calculate the derivative  of the following.

Q: t=a v= t = 1 t = 2 t = 3 v = || V = m/s m/s m/s m/s

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Q: T = Find the equation of the tangent line to the curve when t 6

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Q: Complete the sentence below. Iff is a one-to-one function and f(3) = 6, then f(6) = If f is a…

A: One one functions