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Using rules of logarithms: 3log(x^2)+4log(y^3)=log((x^2)^3)+log((y^3)^4) =log(x^6)+log(y^12) =log((x^6)(y^12)

I would get the student to draw a diagram of the situation.. so draw the curve y=x^2, the tangent at (2,4) and then the normal. Then I would highlight to them that the equation we want is the equation of ...

Differentiation allows you to find the rate of change of a variable relative to another, which is basically the gradient. So if you had a speed-time graph, finding the amount that speed changes over a giv...

First, what is a tangent? A line which touches a circle (or ellipse) at just one point. In our case (-3,2)
As it touches the line at one point, it is perpendicular the radius at (-3,2). Which implies...

The gradient of the line L is -2 so the gradient of the line perpendicular to L will be the negative reciprocal of -2 which is 1/2.The equation of the line perpendicular to L will be y=mx+c where m is the...