How do i differentiate the equation y = x^2 + 6x + 2 with respect to x.

So lets have a quick recap of differenciation to start off. In informal terms, differenciation is carried out by dropping the power to be in front of the term we are differenciating to as well as decrementing the power. So in practice, x^3 would differenciate to 3x^2 when differenciating in terms of x.

We drop the power (being 3) so that it is in front of the term (3x). Then decrement the power (so x^3 becomes x^2). Putting it all together, we get the result 3x^2. Similarly, if we were to differenciate 2x^3. We would obtain (2)(3)x^2 being 6x^2. Don't forget to multiply your result by the number that was in front previously! Which in this case was 2 being in front of x.

Now lets look at the question in hand, lets differenciate each term separately and add them up.

1. x^2 would become 2x^1 if we were to drop the power and decrement the power. 2x^1 is easily rewritten as 2x

2. 6x. This is actually 6x^1. So if we again drop the power and decrement the power, we obtain 6x^0. Which is 6

3. Lastly, 2 which is actually 2x^0. So if we do the same again, we get 0x^-2. 0 multiplied by anything is 0. Therefore 2 differenciated with respect to x is 0.

Adding up add the differenciated terms results in 2x + 6 + 0. So dy/dx = 2x + 6.

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