derivatives...?

Question

how do you find (d^2 y) / (d x^2) of a function?
thanks

Answer 1

well...both answers that were given arnt wrong...but not entirely right

ok...so you are given some equation you find its derivitive

im going to assume you now have solved for dy/dx ...in other words you have an equation

dy/dx = mess of an equation...most likely a fraction

ok, so now you need the second derivitive...if your dy/dx has some y's involved on the right of the equal sign your probably panicking...dont

take your derivitive..probably involving the quotient rule, and when you take derivitives of things with a y in them remember to put the dy/dx

so your final equation will be

d2y/dx2 = some x terms, some xy terms...maybe a fraction and probably some stuff with dy/dx's attached

and you say...now what do i do...well you already know what dy/dx is..you solved for it initially...its the first derivative with respect to x

you now can substitute your dy/dx equation anywhere you see a dy/dx...and some cancelling will ensue...and life will be good

hope this helped

matttlocke

Answer 2

d^y/dx^2 is the second derivative of the function y with respect to x.

dy/dx is the first derivative of y wrt x.

to find the second derivative d^2y/dx^2, just find d/dx of dy/dx.

Eg: y=x^3+4x^2
dy/dx=3x^2+8x
d^2y/dx^2=6x

Answer 3

The same way you find the first derivative.
(d^2 y)/(d x^2) just means it is the second derivative of y with respect to x
Step 1: Find the first derivative.
Step 2: Find the second derivative (this is just the derivative of the first derivative).
Example: Let y = x^5 + 7x^3 - 5x^2 + 1
dy/dx = 5x^4 + 21x^2 - 10x
(d^2 y)/(d x^2) = 20x^3 + 42x - 10

Answer 4

Take to derivative twice.

y = x³
y' = 3x² + C [dy/dx]
y'' = 6x + Cx + D [d²y/dx²]