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Degree: Actuarial Sciences (Masters) - Manchester University
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We recognise that this is in the form of a function within a function, i.e u= 3x - 2 is within the u^4 function, therefore here we will use the chan rule to differentiate the equation.
The chain rule states that dy/dx = dy/du * du/dx.
Here let u = 3x -2, then du/dx = 3. Similarly, y=u^4 so dy/du = 4u^3. Therefore dy/dx = 3 * 4u^3 = 12u^3.
Finally, we substitute u = 3x - 2 into the equation. This therefore gives us, dy/dx = 12(3x - 2)^3.see more
Ok so we need to get 'y' by itself on the left hand side of equal sign. We will first try to remove the denominator by multiplying 'x' by (3+4y). This gives (3+4y)x = 1 - 2y.
We will then expand the brackets so we can get a sum of the single terms i.e this gives 3x + 4yx = 1 - 2y.
We will now gather all terms with 'y' on the left hand side of the equal sign. This gives 4yx + 2y = 1 - 3x.
Now we factorise to get a single 'y' term, this gives (4x +2)y= 1 - 3x.
We finally try to get 'y' on its own by divinding both sides of the equal sign by (4x +2). This therefore gives us y = (1-3x)/ (4x +2) which is our final answer!see more