1. **State the problem:** Find the derivative of the function $$f(x) = \sin x \tan x$$. 2. **Recall the product rule:** If $$f(x) = u(x)v(x)$$, then $$f'(x) = u'(x)v(x) + u(x)v'(x)$$. 3. **Identify components:** Here, $$u(x) = \sin x$$ and $$v(x) = \tan x$$. 4. **Find derivatives:** - $$u'(x) = \cos x$$ - $$v'(x) = \sec^2 x$$ (since derivative of $$\tan x$$ is $$\sec^2 x$$). 5. **Apply product rule:** $$f'(x) = u'(x)v(x) + u(x)v'(x) = \cos x \tan x + \sin x \sec^2 x$$. 6. **Conclusion:** The derivative is $$f'(x) = \cos x \tan x + \sin x \sec^2 x$$. 7. **Match with options:** This corresponds to option (e). **Final answer:** $$f'(x) = \cos x \tan x + \sin x \sec^2 x$$.