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Step 1:

We begin solving this problem by finding the gradient of the tangent line at H, which is equal to dy/dx.

In this case, our curve has equations  x = 3sinθ and ...

Step 1:

When asked to exrpess something in partial fractions, we first compare the power of the numerator to the power of the denominator.

In our case we have that th...

When thinking about stationary points, it is important to remember that these points happen when the gradient of the curve is 0 (-> dy/dx = 0), or if you prefer, when the rate of change of a graph is 0...

y = x²(cos(x)) therefore we will need to use the product rule, 

dy/dx = u dv/dx + v du/dx

where u = x² and v = cos(x)

du/dx = 2x and dv/d...

Differentiation can be done term-by-term, so we can treat the 5x³, -2x² and 2 separately. We can also 'take out' the coefficients: to differentiate 5x³, for example, di...