The discussion centers on differentiating the function \(2^{\sin(\pi x)}\) without using natural logarithms. The correct approach involves recognizing that \(\ln 2\) is a constant and can be left in the expression while applying the product rule to differentiate \(\sin(\pi x)\). The solution simplifies to \(y' = e^{\sin(\pi x) \ln 2} \cdot \frac{d}{dx}[\sin(\pi x)] \cdot \ln 2\). This method effectively resolves the differentiation challenge presented in the homework statement.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation techniques, as well as educators looking for examples of common pitfalls in applying the product rule.
Feodalherren said:Homework Statement
[itex]2^{Sin(PiX)}[/itex]
Homework Equations
The Attempt at a Solution
= [itex]e^{\sin(\pi x)ln2}[/itex]
##y'= e^{\sin(\pi x)ln2}\frac d {dx} [\sin \pi x] \ln 2##
and I'm stuck... The product rule will automatically lead to to differentiating ln 2.