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When faced with a problem like this, it is always a good idea to draw a rough sketch of what might be going on. With the help of a diagram, we notice that PNT is a right angled triangle w...

First we need to make sure we understand implicit differentiation. As we are differentiating with respect to x, y has to be treated differently, this is because it could be anything from a constant to a f...

For simplicity first rewrite as y=(4+3x)/(5-x). Now swap any x for a y, and any y for an x. This leaves the equation x=(4+3y)/(5-y). Our goal is to make y the subject of the formula. Multiply both sides b...

6x + xdy/dx + y + 2ydy/dx - 4 - 6dy/dx = 0xdy/dx + 2ydy/dx - 6dy/dx = 4 - 6x - ydy/dx (x + 2y - 6) = 4 - 6x - ydy/dx = (4-6x-y)/x+2y-6)

a) It is useful to rewrite the equation using power rules, so we get y = 2x³ + 3x^-2Now we can simply use the differentiation rules where we multiply the coefficient (number before x)...