Search over 10,000 free study notes

Let u = x²+4x+2 so y = ln(u).

Then dy/du = 1/u and du/dx = 2x+4.

Using the chain rule we have:

dy/dx = (dy/du)*(du/dx)

= (1/u)*(2x+4)

= (2x+4)/(x²+...

In order to find the nth term of a sequence you need to keep the structure of the nth term sequence in mind (dn+x). The first thing we want to do is find 'd'. In this case 'd' stands for difference, which...

These problems can be tricky as they use unfamiliar trigonometric functions such as secant and cosecant. It is much easier to approach these problems by replacing these trigonometric functions with more f...

A cuboid has sides such that the longest side is two units more than the shortest side, and the middle length side is one unit longer than the shortest side. The total surface area of the cuboid is 52 uni...

We know from simple fraction rules that dy/dx=(dy/dt)/(dx/dt). dy/dt=2t, dx/dt=3t^2+1. Therefore, dy/dx=2x2/12+1=4/13