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finding the second derivative?
Find (d^2y/dx^2)
1. 4x^2+wy-3y=5
2. 2x^3-2xy+4y^2=3
3. 3x^2-xy+3y^2=1
I'm sick and missed class... these were the problems my teacher used to review finding 2ed derivatives in class.. could you help me out and explain some of the steps?
Thanks!
2 Answers
- Sridhar RLv 61 decade ago
I hope you have done implicit differentiation
see the tutorial given below
I am solving 2 question rest are similar you can do it and verify with your answer
2) 2x^3 -2xy + 4y^2 =3
First order
6x^2 - (2y+ 2x dy/dx) + 8 ydy/dx =0
6x^2 -2y +dy/dx( 8y -2x) =0 ------------------------------(1)
dy/dx = (2y - 6x^2) / (8y -2x) ----------------------------- Ans
Second order
it is easier to differentiate eqn(1) to get second order
12x - 2dy/dx + d^2y/dx^2(8y - 2x) + dy/dx ( 8dy/dx -2)
d^2/dx^2 (8y -2x) = -12x -4dy/dx + 8(dy/dx)^2
- 1 decade ago
I am going to assume you know how to do basic derivatives.
1. we will take dy/dx= 8x then we will take d^2y/dx^2=8
2. dy/dx=6x^2-2y then we will take d^2y/dx^2=12x
3. dy/dx=6x-y then we will take d^2y/dx^2=6