We don't have a formula for y. We could solve this equation for y, but we would find ![](https://media1.shmoop.com/images/calculus/cal_compderiv_implct_narr_latek_11.png)
which is two equations. We would then take two separate derivatives, and that's too much work. Instead, take derivatives of both sides of the equation, with respect to x: ![](https://media1.shmoop.com/images/calculus/cal_compderiv_implct_narr_latek_12.png)
Since the derivative of a sum is the sum of the derivatives, and the derivative of a constant is 0, ![](https://media1.shmoop.com/images/calculus/cal_compderiv_implct_narr_latek_13.png)
Pause for a minute. While we don't have a formula for y, we know that y is a function of x. That is, y is the inside function and (□)2 is the outside function. To take the derivative of y2 we need to use the chain rule: ![](https://media1.shmoop.com/images/calculus/cal_compderiv_implct_narr_latek_14.png)
Put this back in the equation where we left off: ![](https://media1.shmoop.com/images/calculus/cal_compderiv_implct_narr_latek_74.png)
It's like magic. In the original equation we had a messy y2 term, but now we have dy/dx. Solving for the derivative, we find ![](https://media1.shmoop.com/images/calculus/cal_compderiv_implct_narr_latek_75.png)
In this type of problem, it's fine to have y in the definition of the derivative. We can't write y in terms of x since we don't have a formula for y in the first place. The final answer is ![](https://media1.shmoop.com/images/calculus/cal_compderiv_implct_narr_latek_76.png)
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