SUMMARY
The derivative of the function f(x) = sin x + 2 cos^3 x is f'(x) = cos x - 6cos^2 x sin x. The initial mistake in the calculation involved incorrectly applying the power rule instead of the chain rule. The correct application of the chain rule, d/dx[f(g(x))] = f'(g(x))g'(x), clarifies the derivation of the sin x term in the final answer.
PREREQUISITES
- Understanding of basic derivative properties
- Familiarity with the chain rule in calculus
- Knowledge of the power rule for derivatives
- Ability to differentiate trigonometric functions
NEXT STEPS
- Review the chain rule in calculus
- Practice differentiating composite functions
- Explore the power rule and its applications
- Study trigonometric derivatives and their properties
USEFUL FOR
Students studying calculus, particularly those learning about derivatives and trigonometric functions, will benefit from this discussion.