find dy/dx when y=6t^2 where t=-6/x?

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2007-04-23 20:17:05 · 4 answers · asked by october_rose01 1 in Science & Mathematics ➔ Mathematics

dy/dt = 12t = -72/x

dt/dx = 6/(x^2)

dy/dx = dy/dt . dt/dx = -432/(x^3)

2007-04-23 20:23:04 · answer #1 · answered by gudspeling 7 · 1⤊ 0⤋

by chain rule:-
dy/dx = dy/dt * dt/dx

y = 6t^2
dy/dt = 12t = 12(-6/x) = -72/x

t=-6/x
dt/dx = 6/x^2

therefore, dy/dx = (-72/x) * (6/x^2) = -432/x^3

2007-04-23 20:37:50 · answer #2 · answered by eve88 2 · 0⤊ 0⤋

y = 6 t² and x = - 6.t^(-1)
dy/dt = 12t and dx/dt = 6.t ^(-2) = 6 / t²
dy / dx = 12t / (6 / t²)
dy/dx = 2.t³
or
dy/dx = 2.(- 6/x)³ = - 432 / x³

2007-04-23 20:34:22 · answer #3 · answered by Como 7 · 0⤊ 0⤋

y = 6 t^2 = 6 (-6* x^-1)^2
y = 216 x^(-2)

dy / dx = -2*216 x^(-3)= -432 x^(-3)

2007-04-23 20:27:56 · answer #4 · answered by Anonymous · 0⤊ 0⤋