X - 2 at2- y - 4 at Find d2ydx2-

Given , #160; #160; #160; #160; #160; x=2at^2dxdt=4at #160; #160; #160; #160; #160; y=4 #160; #160;dydt=0 dydx=( ...

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Chain Rule of Differentiation

x = 2 at2, y ...

Question

$x = 2 a t^{2}, y = 4$ at Find $\frac{d^{2} y}{d x^{2}}$ .

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Solution

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x = 2 {a t}^{2}, y = {a t}^{4}

\frac{d^{2} y}{d x^{2}}

t = 2

x = a t^{2}, y = 2 a t

\frac{d^{2} y}{d x^{2}} = \frac{- 1}{2 a t^{2}}

x = a t^{2}

y = 2 a t

\frac{d^{2} y}{d x^{2}}

x = 3 tan t

y = 3 sec t

\frac{d^{2} y}{d x^{2}}

t = \frac{π}{4}

x = a {cos}^{3} θ, y = a {sin}^{3} θ

\frac{d^{2} y}{d x^{2}}

θ = \frac{π}{4}

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