Differentiate (with respect to x), y=2x^2+8x+5.

y= 2x^2 + 8x + 5 is a simple quadratic equation and can be easily differentiated. Consider it in different terms working from left to right: y converts to dy/dx. This just means ‘differentiate y with respect to x’ and is how we show we have differentiated the equation.
For the rest of the terms simply multiply the power that the x has by the number before the x and then minus 1 from the power. I.e. 2x^2 = (2x2)x^(2-1) = 4x^(1)=4x. Next term, 8x = 8x^1 = (8x1)x^(1-1) = 8x^0 = 8. Finally, 5 = 5x^0 = (5x0)x^(0-1) = 0. Notice how I have added powers that you would not normally show for explanation but you do not need to show this when writing in the exam. Also remember that x^0 is always 1.
Therefore replacing the original terms with the differentiated terms, we get:
dy/dx = 4x + 8 + 0 = 4x + 8