Question

Giving the function find the answer

Answer 1

Your answer should be -2x

Explanation:

I am not sure if your teacher taught you the short cut way of doing derivatives yet.

That equation is just a long way to do derivatives. The picture below shows the shortcut way to do dervatives.

So basically you plug in x+h into the equation given to you.

`(g(x+h)-g(x))/(h) \\\\((6-(x+h)^2)-g(x))/(h) \\\\((6-(x^2+2xh+h^2))-(6-x^2))/(h)\\\\ ((6-x^2-2xh-h^2)-(6-x^2))/(h)\\\\ (6-x^2-2xh-h^2-(6-x^2))/(h)\\\\ (6-x^2-xh-h^2-6+x^2)/(h)\\\\`

`((x^2-x^2)+(6-6)-2xh-h^2)/(h)\\\\ ((0)+(0)-2xh-h^2)/(h)\\\\ (-2xh-h^2)/(h)\\\\ (h(-2x-h))/(h)\\\\ -2x-h`

Plug in h = 0

then your answer is -2x