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e^x sin(x) is a product of two functions: e^x and sin(x). This means we can use the product rule.
Let e^x = u and sin(x) = v
The differential of uv is u'v + v'u whe...

2 simultaneous unknown equations. Let x be the number of apples originally, and n the number of fruits in the bag in total originally. i) first scenario, where probability is 1/5, x/n = 1/5    5x= n  ii) ...