Search over 10,000 free study notes

dy/dx = (4cos(2x) + 6sin(2x) + 2)/(2+cos(2x))²

First, write y in terms of cos(x). We are familiar with cos(x) and know how to differentiate it. We know that sec(x) = 1/cos(x) = (cos(x))^-1.  Next, find dy/dx in terms of cos(x) and sin(x). Ag...

In order to solve this inequality, it is helpful to have all the terms on the left-hand side of the equation. To do this, we can subtract 3(x + 6) from both sides of the equation. This gives us:

x^...

Here we must use the product rule to differeniate because x appears in both terms of the equation, therefore both parts must be differentiated. So we will set u= x² and v= (5x-1)^(1/2) written ...

To find the derivative of two functions multiplied by each other we would use the product rule.

The product rule: (fg)'(x) = f '(x).g(x) + f(x).g'(x)

First we need to split our function into...