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We will be using the quotient rule, although the product rule is also usable and can be run through if the student wishes. Firstly, define u = 8x, v = x-8 for simplicity. Then clearly u' = 8, v' = 1, and ...

For this we must use the chain rule. We start by defining x³ as a new variable, u = x³ Can then rewrite the expression as y = sin(u) Chain rule tells us that dy/dx = (dy/du)(du/dx) W...

2y=11-3x    and 2y=2x-14

11-3x=2x-14

25=5x   thus x=5

3(5) +2y=11

2y=-4    thus y=-2

Expansion of the given expression will result in x to the 3rd power, as there are 3 parts involving x, multiplied together. Let's ignore -5x for a second, and multiply the two expressions in brackets (usi...

As both equations are equal to y, we can combine them to create a single equation in terms of x: x^3 - x^2 -5X + 7 = x + 7. Shift the equation so the left hand side is equal to 0 on the right: x^3 - x^2 -...