Final answer:
The student's question concerns the differentiation of the function f(x) = (x³tanx) / (-2secx), which involves applying the quotient rule in combination with the product rule and the chain rule.
Step-by-step explanation:
The question appears to be asking for the differentiation of the function f(x) = (x³tanx) / (-2secx). To differentiate this function, we'll need to apply the quotient rule and the chain rule. The quotient rule is used when differentiating a function that is the ratio of two other functions, which in this case are the numerator x³tanx and the denominator -2secx. The chain rule is used to differentiate composite functions.
The differentiation steps will include:
- Differentiating the numerator which will involve using the product rule because it contains two functions multiplied together (x³ and tanx).
- Differentiating the denominator which is a simple derivative of a secant function multiplied by a constant.
- Applying the quotient rule where the derivative of the function will be the derivative of the numerator times the original denominator minus the original numerator times the derivative of the denominator all over the square of the original denominator.
Remember to also simplify the final expression to find the simplest form of the derivative.