differentiate the equation f(x) = 3x^2+5x+3

Look at each of the x variables to determine what happens to each term.

3x^2 has a power of 2 on the variable, therefore, the 2 is multiplied by the coefficient on the x. You must also subtract 1 from the value of 2 on the indices. This leaves you with 6x^1 which can be written as 6x. 

The same must be done for 5x, however as the 3 has no x variable, it is not present in dy/dx