Search over 10,000 free study notes

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...

 To differentiate this function we use the product rule. In the product rule we, leave the first alone, differentiate the second, and leave the second alone, differentiate the first.                      ...