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(This is a common question in C4, the "hardest" module of the old A level)When differentiating we consider each term one at a time:Differentiating 3x² simply gives us 6x Differentiati...

We are looking for a straight line, so it needs the form y=mx+c. To find our gradient, m, we need the gradient of the curve at the point x=-2, so differentiate the equation: dy/dx=6x²+6x-4, and...

The formula for integration by parts is Integral(udv/dx)dx = uv - Integral(vdu/dx)dx
You use integration by parts when you have an integral where you have to terms multiplied together ie Int...

16y³ + 9x²y - 54x= 0 
a) Differentiate the terms separately dy/dx(16y³ + 9x²y - 54x) = dy/dx(16y³) + dy/dx(9x²y) - dy/dx(54x) ...

0.5Ln(x^2+2)+ C