## anonymous 5 years ago i am getting confused with integrating and differentiating :S how can i tell the difference and what do they find? and what is a second derivative ?

1. anonymous

you just remember this one differentiate = finding derivative = finding the instantaneous slope usually the notation is $d/dx (fx)$

2. anonymous

or $dy/dx$

3. anonymous

or

4. anonymous

y'

5. anonymous

i want to know about equations, not the actual graph

6. anonymous

Integrating = anti derivative = area under the curve so it looks like$\int\limits f(x) dx$

7. anonymous

double derivative or the second derivative means that you take the derivative of the derivative

8. anonymous

so it is as same as saying $d/dx (d/dx (f(x)))$

9. anonymous

what do these things work out? gradient?

10. anonymous

11. anonymous

the common notations are$d^2/dx^2 (f(x))$

12. anonymous

or y"

13. anonymous

SO WHAT DO THEY WORK OUT?!?!? WHICH ONE IS THE GRADIENT ONE AND ISNT ONE OF THEM FOR THE STATIONARY POINTS?!?!? ANYONE?!?!?! pwetty pwease

14. anonymous

They 'work out' the slope. The derivative of an equation at a point gives you the slope of the tangent line at that point. They are also used to calculate the area under a curve.

15. anonymous

ok, is that the for the first or second one tho? :S

16. anonymous

Either. A second derivative calculates the slope of a tangent line of the first derivative.

17. anonymous

sorry but i dont get it so there isnt a difference?

18. anonymous

The second derivative is the derivative of the first derivative. The equations are different, but any derivative - 1st, 2nd, 3rd, Nth, is determining the slope of the tangent line of the (n-1)th derivative.