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find, from first principles, the derivative of y= (sinx)(e^x)

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\[\frac{ dy }{ dx }= \lim_{h \rightarrow 0} \frac{e ^{x+h} \sin(x+h) - e^{x} sinx}{h}\]
Maybe try an angle sum identity for sin(x+h), and for e^{x+h}, you add the exponents when multiplying powers of the same base. See if you can use that to factor things out.
i did the question till, \[\lim_{h \rightarrow 0}\frac{e^x e^h sinx \cosh + e^x e^h cosxsinh -e^xsinx}{h}\] but i can't eliminate the terms

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add some increment to both sides.

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