Find dy/dx at t=3, where x=t^3-5t^2+5t and y=2t^2
Using the product rule, we find that dy/dx= dy/dt multiplied by dt/dx, where dt/dx is the reciprocal of dx/dt
dx/dt= 3t^2-10t+5, dy/dt= 4t
At t=3, dx/dt= 3(3)^2-10(3)+5=2, dy/dt= 4(3)= 12
Therefore, dt/dx= 1/2
dy/dx= dy/dt x dt/dx= 12 x 1/2= 6
OA
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