y = 3x^2 + 2x^(1/2) - 12 Find dy/dx

Firstly we divide up the equations into its three compenents based on the powers of the x values, giving us 3x^2, 2x^(1/2) and -12. Now one at a time, we multiply the coefficient by the power of x, and then subtract one from this power. For each component we get:

Multiply by power (2):   3x^2 * 2 = 6x^2     Subtract 1 from power:  2-1=1 --> 6x

Multiply by power (1/2):   2x^(1/2) * 1/2 = x^(1/2)     Subtract 1 from power:   (1/2 - 1 = -1/2) --> x^(-1/2) or 1/x^(1/2) as power is negative.

With the final component we can save our selves time by knowing that if you differentiate any number that isnt multipled by a variable, in this case x, it simply equals zero. This is because we view the number as being a coefficient of x^0, hence our first step is multiplying by zero.

The final answer is :  dy/dx = 6x + 1/x^(1/2)