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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) ...

to find dy/dx, multiply each item by the power of the x, and then decrease the power of the x by 1.Step 1 : 2x^2 -15x (multiplying by power of x)Step 2 : 2x^1 -15x^0Therefore:dy/dx = 2x ...

Begin by multiplying the second equation by three in order to get a 3y value: 9x + 3y = 33. We can now subtract equation one from equation two, 9x + 3y = 33 and 2x + 3y = 19 -->7x + 0y = 14. Resulting ...