Forgetting to apply the chain rule when differentiating composite trigonometric functions like sin(2x) or cos(x^2).
Differentiation rules only apply where the function is defined and continuous; overlooking domain restrictions can lead to incorrect results.
Remember to apply the chain rule correctly to each term involving y and to express dy/dx in terms of x and y.
Ensure both dx/dt and dy/dt are correctly computed before finding dy/dx, and remember to express the final answer in terms of x or y if required.
Forgetting to differentiate both sides of the equation with respect to x after taking logarithms, leading to an incomplete derivative.
Neglecting the chain rule when differentiating functions like e^(f(x)), where f(x) is a function of x, leading to incorrect derivatives.
Considering the different cases where the expression inside the absolute value is positive or negative, as the derivative changes at the point where the expression equals zero.
Misapplying or confusing these rules can lead to significant errors, especially when dealing with complex expressions involving multiple functions.