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Here we have a function made from the product of two functions, so we canuse the product differenciation rule.
y=uv => dy/dx=udv/dx + vdu/dx
Therefore dy/dy=(x-2)^2 + 2(x-2)(x+1)
6a + b = 16 (1)
5a - 2b = 19 (2)
(1) x 2: 12a + 2b =32
(1) + (2): 12a + 2b + 5a - 2b = 32 + 19 = 51
17a = 51
a = 51 / 17 = 3
Substitue a = 3 back into (1): (6 x 3...
Now although this might seem like quite a complex question at first, it's a little less intimidating when we take a while to look at it- you might notice that we can seperate x and y terms like so:1...
0= (x + 4)(x + 1)
x= - 4
x= - 1
lnx differentiates to 1/x
4x^2 differentiates to 8x
3e^4x differentiates to 12e^4x
therefore the answer is: 1/x + 8x + 12e^4x
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