Question

use the definition of the derivative to calculate f'(8) where f(x) = x+3

Answer 1

i really need help understanding derivatives! Please show me the process so I can understand it better! Thanks!

Answer 2

To find the derivative of x+3, we take the derivative of x plus the derivative of 3. The derivative of 1x is just one (The x is raised to the 1st power. When you find the derivative, we lower the exponent by one, and multiply by the old exponent. This gives us x^0 which is just 1, which eliminates the x from the problem). The derivative of any constant is 0, so the derivative of +3 is 0. Thus, our derivative is:
f'(x)=1 for any value of x. So the answer is 1.

Remember that the derivative just tells us the slope of the original function at any given point. Since our equation was a straight line with slope 1, it makes sense the derivative is always 1.