SUMMARY
The derivative of the function f(t) = te^(2-7t) is calculated using the product rule and the chain rule. The correct application of these rules yields f'(t) = t * d/dt(e^(2-7t)) + e^(2-7t) * d/dt(t), resulting in the final answer of f'(t) = e^(2-7t)(t * -7 + 1). The key steps involve differentiating the exponential function and applying the product rule correctly.
PREREQUISITES
- Understanding of the product rule in calculus
- Knowledge of the chain rule in calculus
- Familiarity with exponential functions
- Basic differentiation techniques
NEXT STEPS
- Review the product rule and its applications in calculus
- Study the chain rule and practice differentiating composite functions
- Explore exponential function properties and their derivatives
- Practice solving similar derivative problems involving products of functions
USEFUL FOR
Students studying calculus, particularly those learning about differentiation techniques, as well as educators looking for examples of applying product and chain rules in derivative calculations.