If a problem gives you a function f(x) and says to find f'(x). Then says to find a reasonable way to simplify the result to find f''(x), does that mean you need to find the derivative of f(x), and that would equal f'(x). Then to find f''(x), you would have to look for the derivative of f'(x)?

Would that be how you find f'(x) and f''(x)?

Thank you!

Question

If a problem gives you a function f(x) and says to find f'(x). Then says to find a reasonable way to simplify the result to find f''(x), does that mean you need to find the derivative of f(x), and that would equal f'(x). Then to find f''(x), you would have to look for the derivative of f'(x)?

Would that be how you find f'(x) and f''(x)?

Thank you!

hartnn · Answer

yes, thats probably the most standard method to do it.

anonymous · Answer

oh okay great!

so kinda like this?

f ' (x) = the derivative of f(x)

f '' (x) = the derivative of f ' (x) 

^^the simpler way of saying what i wrote above hahaa

hartnn · Answer

yes, and thats absolutely correct :)

anonymous · Answer

yay!!! thanks so much :)

hartnn · Answer

any specific example you need help on ?

anonymous · Answer

not at the moment :)

i just wanted to check if i understood it correctly.. i'm studying notes right now and it wasn't too clear about that part :)

thanks again!!

whpalmer4 · Answer

Another form of notation commonly seen is 

$$y = f(x) = \text{original function}$$$$\frac{dy}{dx} = f'(x) = \text{1st derivative of original function}$$$$\frac{d^2y}{dx^2} = f''(x) = \text{2nd derivative of original function} $$$$\qquad = \text{1st derivative of }f'(x)$$$$\qquad=\text{1st derivative of }\frac{dy}{dx}$$Etc.

anonymous · Answer

oh okay, awesome!! thank you! :)