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