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Firstly we must notice that we can differentiate each term separately.

Starting with the 2xy term, we must use the product rule as x and y are two variable that will differentiate. Setting u=2x and...

In order to rationalise the denominator we need to get rid of the surd (square-root) on the bottom of the fraction.

To do this, we can multiply the denominator by sqrt(5).

But we must notice...

We want to determine whether a function has a tangent which is horizontal. To answer the question we need to know what a horizontal tangent to a function means. A tangent to a graph of a function is a lin...

To see where the graph is greater than zero, we start by finding where it meets zero. By factorising (x^2 - 7x - 18), we find it equals (x-9)(x+2). The expression equals zero at the points x = 9 and x = -...

Since y is equal to both 5-x and to x+1, we know that 5-x is equal to x+1. We can write 5-x=x+1. Take 1 away from each side: 4-x=x. Then add x to each side: 4=2x. Divide both sides by 2: 2=x. Now we have ...