what is the n times differentiation of $e^{3x}\cdot \sin^2x$ I have an equation y = $e^{3x}\cdot \sin^2x$ and I want to calculate n times differentiation of it. As it is in the form of uv so I am lost here because at every iteration more term will generate and I don't know how to handle these kind of differentiation. My questions are -


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*What is the solution of this problem?


*Are there any general rules for solving this kind of $n$ times differentiation?

Please provide step by step solution and proper references.
Edited:
If Leibniz formula can solve this problem then please suggest me some good book  where there will be some good examples so that I can understand it well.

One way is to use the leibniz formula $$D^n(fg) = \sum_{k=0}^n {n \choose k} D^k(f) D^{n-k}(g).$$ You can easily compute $$D^{n-k}(e^{3x}) = 3^{n-k}e^{3x}$$ and $$D^{k}(\sin^2(x))=D^k\left(\frac{1-\cos(2x)}{2}\right).$$ For this last derivative you have to discuss the parity of $k$, can you finish that ?
