Answer:
-ln 3
Explanation:
The instantaneous rate of change of f(x) at x = π is the derivative of this function at x = π.
We know that
[tex]f(x)=3^{sinx}[/tex]Then, the derivative is
[tex]\begin{gathered} f^{\prime}(x)=3^{sinx}(\ln3)(\sin x)^{\prime} \\ f^{\prime}(x)=3^{sinx}(\ln3)\cos x \end{gathered}[/tex]Now, we can replace x = π to get:
[tex]\begin{gathered} f^{\prime}(\pi)=3^{\sin\pi}(\ln3)(\cos\pi) \\ f^{\prime}(\pi)=3^0(\ln3)(-1) \\ f^{\prime}(\pi)=(1)(\ln3)(-1) \\ f^{\prime}(\pi)=-\ln3 \end{gathered}[/tex]Therefore, the instantaneous rate of change is -ln 3
