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(x-4x³) = x(1-4x²)  Just taking a factor of x out of both terms Within the inner bracket we have a difference of two squares. 1²=1 and (2x)²=4x² ther...

First step is to seperate the variables (EQ1) : (1/y^2) dy = 6x   Then we integrate each side seperately giving us (EQ2) : -1/y = 3x^2 + C (remembering to add 1 to the power and divide by the new power) s...

I would differentiate it and then turn it into an equation to find the points where the gradient equals zero. With these points at hand, I would take a second derivative, this tells me how the gradient ch...

(a)  9x+11/(2x+3)(x-1) = A/2x+3 + B/x-1
      9x+11 = (x-1)A + (2x+3)B
      Setting x=1 gives B=4, setting x=-3/2 gives A=1
      so the final answer is 1/(2x+3) + 4/(x-1)
 

y = e^xx² + e^x   : The derivative can be found using the chain rule. (A reminder of the chain rule: if y is a product of two funct...