Determine the first derivative of the following curve defined by parametric equations x = 20-5t and y = t^5.
First remember that a parametric curve z = (x(t), y(t)) can be differentiated using the following formula (derived using the chain rule): dz/dt = (dy/dt)/(dx/dt). We should now find dy/dt and dx/dt (which are immediate)dx/dt = -5; dy/dt = 5t^4and it follows (using the formula above) that the desired derivative is dz/dt = (5t^4)/(-5) = -t^4
FC
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