Find dydx- where x-3at1-t3- y-3at21-t3

x=3at1+t^3, y=3at^21+t^3⇒yx=t ⇒ x=3ay/xx^3+y^3x+2⇒ x^4+y^3x= 3ax^2y ⇒ 4x^3+y^3+3y^2xdydx= 6axy+3ax^2dydx ⇒dydx=4x^3+y^3 6axy3ax^2 3xy^2 ...

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Parametric Differentiation

Find dydx, w...

Question

Find $\frac{d y}{d x}$ , where $x = \frac{3 a t}{1 + t^{3}}, y = \frac{3 a t^{2}}{1 + t^{3}}$

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Solution

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x = \frac{3 a t}{1 + t^{3}}

y = \frac{3 a t^{2}}{1 + t^{3}},

\frac{d y}{d x}

x = \frac{3 a t}{1 + t^{2}}, y = \frac{3 a t^{2}}{1 + t^{2}}

\frac{d y}{d x}

\frac{d y}{d x},

x = 3 a t

y = 3 a t^{2}

\frac{d y}{d x}

x = a t^{2}, y = a t - t^{3}

x = \frac{a}{1 + t^{3}}, y = \frac{a t}{1 + t^{3}}

\frac{d y}{d x}

t = 1

\frac{1}{p}

p =

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