Find dy/dx if y=3x+5

Question

Find dy/dx if y=3x+5

Answer 1

I noticed that another tutor already answered by using the power rule, however it may be the case that you have not learned the general power rule in class yet, and that you are supposed to use the limit definition of the derivative.

In that case you are given the following: y(x) = 3x + 5

Then by definition dy/dx = lim_{h —> 0} (y(x + h) - y(x))/h

which we can then plug in the function to get:

dy/dx = lim_{h —> 0} (3(x + h) + 5 - (3x + 5))/h

= lim_{h —> 0} (3x + 3h + 5 - 3x - 5)/h

= lim_{h —> 0} 3h/h = 3

This works because in a limit h/h = 1 so we can simplify it out to just be 3*1 = 3

Answer 2

Power Rule

For a real number n, the derivative of y = xⁿ

dy/dx = n x ^n-1

You can think of yours as y=3x¹+5x⁰

So applying the power rule

dy/dx = (3)(1) x^1-1 + (5)(0)x^0-1 Simplify

dy/dx = 3x⁰+ 0 Simplify

dy/dx = 3