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Using the chain rule, differentiate the "outside function" and the "inside function", and multiply the two results to get:dy/dx = 4(x-1)^3 * 1 = 4(x-1)^3

We know that dy/dx = (dy/dt) * (dt/dx). Differentiating each of the equations with respect to t gives. dy/dt = sec(t) tan(t) and dx/dt = sec²(t). Since dt/dx = 1 / (dx/dt) we have that dt...

There are three methods to solve these types of silmultaneous equation questions, substitutution, elimination and matrices. In this example we use substitution and elimination.Elimination example.Eq1). 7x...

x²+8x +15 = 0
(x+4)²-16 +15=0
(x+4)²-1=0
(x+4)= (+/-)1

x = -3 or -5

The easiest way to do this is to first work out the area of the whole circle. To work out the area of a circle, the equation is area = πr² , w...