Final answer:
To solve for y and find y' in terms of x, one must follow a systematic process of substituting known values into the appropriate equation, solving for y, and then differentiating with respect to x.
Step-by-step explanation:
To solve the equation explicitly for y and differentiate to get y' in terms of x, a step-by-step approach is needed. Initially, the quadratic equation provided should be solved for y. Following that, one would substitute the known values into an equation related to the context, which could be motion (involving initial position, velocity, and acceleration) or another subject, such as thermodynamics or fluids. Once y is explicitly expressed, differentiation can be carried out to obtain y' as a function of x.
solution verification often requires taking derivatives with respect to time and substituting them back into an equation to confirm its validity. Furthermore, reducing a line integral to an integral over a single variable is a common process in integration, which can necessitate solving for one variable in terms of another.
Choosing the appropriate equation and plugging in known values allow for the resolution of unknowns.