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So this function is the product of two functions of x, so we use the product rule to differentiate it. The rule states if y=uv, dy/dx=(du/dx)v+(dv/dx)u. In this function we assign u=(4x+1)³ and...

we have dy/dx = -x/y , so we treat the differentials as fractions and write y dy = -x dx. Now integrating the left side with respect to y and the right side with respect to x, we have y²/2 = -x...

When you differentiate a function which has only one parameter, like f(x), you are finding a new function, f'(x), which gives the gradient of your original function at every point. You'll probably remembe...

Firstly we will put this into a form equal to zero, by rearranging to get x³-2x²-5x+6 = 0. This is because in order to solve a polynomial we first need to set it equal to zero. We no...

Ideally to find the exact area under the curve, we would integrate the function and substitute in the bounds given. However, using the trapezium rule gives an approximation whereby using more trapezia inc...