derivative
posted by Jin .
I am finding the second derivative of (x^2)(y^3) = 1
2x(y^3) + (x^2)(y')(3y^2) = 0
And I simplified the answer to
y'= (2y)/(3x)
so it would be...
[(2y')(3x)(2y)(3)]/(9x^2) and it's simplified to (6xy'+6y)/(9x^2)= y''
I could plug in (2y)/(3x) in place of y'.
The correct answer is y''=(10y)/(9x^2), but I did not get this answer. Please help me!
This looks correct, but you dropped the y'
2x(y^3) + (x^2)(y')(3y^2)y' = 0 so
y'=2x(y^3)/(x^2)(3y^2)=2y/3x
If we now differentiate this again we get
y"=[3x*(2y')(2y)*3]/(9x^2)=(6xy'+6y)/(9x^2)
If we now substitute 2y/3x for y' we get
y"=[(6x*2y/3x)+6y]/9x^2=[4y+6y]/9x^2
Yes, you should make the substitution for y' and you'll get the correct answer in terms of x and y only.
Respond to this Question
Similar Questions

Calculus (Help)
Also I would like to know how to set this problem up in finding the answer: Find the second derivative. y= sqrt(3x+4) Thanks, P.S. I tried taking 3x+4 and squaring it to the 1/2. I thought that might've been the same, then I took the … 
Calculus
R=M^2(c/2m/3) dR/dM=CMM^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? 
Calculus> bobpursley
How do you get m=0? from taking the second derivative? 
Calculus
How would I go about finding the derivative of f(x)=ln(x)(7x2)^3 first=ln(x) second= (7x2)^3 Would I do first times the derivative of the second + second times the derivative of the first? 
Calculus
f(x)=x^3(x^(4)8) Find f '(x) by multiplying out before taking the derivative Is the answer x^12+8+x^128x^3 simplified to 2x^128x^3+16 
Derivatives Math
Can someone explain how to find the derivative of : 1. y= 5^ãx / x And the second derivative of: y= xe^10x For this question I got up to the first derivative and got this y = e^10x + 10xe^10x but I can't seem to get the correct … 
Calcplease help!
What is the second derivative of (x^3)/(x^21)? 
check my work on derivatives
Can someone check my work? So, I took the derivative of (1x^2)/((1+x^2)^2) I used the quotient rule ((2x((1+x^2)^2)2((1+x^2)^2)(2x)(1x^2))) / ((1+x^2)^4) Then I simplified it (2x+2x^2  4x((1+x^2)^2)(1x^2)) /((1+x^2)^4) Then I 
Math
How would I find the derivative of y=cotx with respect to x and also the answer should be in simplified form This is what I got: y= 1/tanx Y= cosx/sinx Idk what to do next 
math
Can someone please check ny answers and tell me if I'm correct?