Forgetting to differentiate the inner function is a frequent error. Students often differentiate the outer function but neglect to multiply by the derivative of the inner function.
Always remember to apply the chain rule when differentiating terms involving y with respect to x, and explicitly include dy/dx. Solve for dy/dx only after differentiating all terms.
Incorrectly applying the derivative rules for trigonometric functions, such as confusing the derivative of sin(x) with -cos(x) or forgetting to apply the chain rule when the argument of the trigonometric function is not simply x.
Ensure you correctly apply the standard derivative formulas for e^x and ln(x), and remember to use the chain rule if the exponent or argument is a function of x. A common mistake is forgetting the derivative of the exponent in e^f(x).
Applying the product or quotient rule incorrectly, especially with regards to the signs and order of terms. Double-check the formula and ensure correct substitution.
Forgetting to find dy/dx by dividing dy/dt by dx/dt, and not expressing the final answer in terms of x alone, if required. Also, be careful when finding the second derivative d²y/dx², remembering to apply the chain rule.
Practice regularly, showing all steps clearly, and double-checking each step for errors. Pay close attention to the chain rule, product rule, quotient rule, and standard derivative formulas. Review past exam papers to identify and address common mistakes.