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The first step is to differentiate the equation of the curve in order to find the gradient of the tangent at the curve. Remember that when differentiating polynomials, we multiply the index of the vari...

The first step is to find dy/dx.

To do this you must first expand the brackets.

x² + y² + 2xy = xy²

Then differentiate each te...

Solve the equation x²=2x (solve x²-2x=0 by factorisation). Sketch the graphs y=x² and y=2x, using standard graph shapes. Look at the sketch to see for which values of x...

Assuming the correct tools of differentiation have been taught, we can tackle each term seperately and then rearrange to have dy/dx as the subject.

Taking a look at the first term, x^2,  ...

Firstly, when approaching a differentiation question you need to work out what method you need to use to solve it. As you can see there are two terms multiplied by one another (the 'x' term and the '(x...