The variable x=t^2 and the variable y=2t. What is dy/dx in terms of t?
This question may seem difficult but we just have to remember the rules of parametric differentiation and the chain rule.
The chain rules states that dy/dx=dy/dz*dz/dx where z is a third variable. Parametric differentiation incorporates the chain rule and states that if x=f(t) and y=g(t), where f and g are both functions of t, then dy/dx=(dy/dt)/(dx/dt).
The first step is to find dy/dt and dx/dt. If y=2t then dy/dt=2 by remembering differentiation rules and if x=t2 then dx/dt=2t.
Now that we have dy/dt and dx/dt, the next step is to find dy/dx using the formula given in the definition. Therefore, dy/dx = 2/2t. The factor of 2 in the numerator and denominator then cancel so we are left with dy/dx=1/t. The question has asked us to leave the derivative in terms of t so we have no more steps left and we have answered the question.
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