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Implicit differentiation to find second derivative
- Thread starter JasCL
- Start date
D
Deleted member 4993
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Use implicit differentiation to find the second derivative at point (9,1) is y is given the function: 6 x y^6 - 10 y^(1/2) = 44 y^2
Help much welcomed
Start with calculating the expression for first derivative - then differentiate again to calculate the second derivative.
What are your thoughts?
Please share your work with us ...even if you know it is wrong
If you are stuck at the beginning tell us and we'll start with the definitions.
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my working so far
well this is my working so far. I think I getting confused when doing the second derivative
6*x*y^6-10(y)^(1/2)=44*y^2
6(xy^6)'-10(y^(1/2))'=44(y^2)'
dy/dx => 6(y^6+6xy^5y')-10((1/2)*y^(-1/2)y')=44(2yy')
6y^6+36xy^5y'-5y(-1/2)y'=88yy'
sub in (9,1)
6+324y'-5y'=88y'
y'=-2/77
Now this is where I think im wrong and getting the wrong answer
d^2y/dx^x=> 6(6y^5y'+6x(y'*5y^5y'+y^5y''))-10(-y^(-3/2)y'+(1/2)y^(-1/2)y'')+44(y'y'+2yy'')
Thanks for the help
well this is my working so far. I think I getting confused when doing the second derivative
6*x*y^6-10(y)^(1/2)=44*y^2
6(xy^6)'-10(y^(1/2))'=44(y^2)'
dy/dx => 6(y^6+6xy^5y')-10((1/2)*y^(-1/2)y')=44(2yy')
6y^6+36xy^5y'-5y(-1/2)y'=88yy'
sub in (9,1)
6+324y'-5y'=88y'
y'=-2/77
Now this is where I think im wrong and getting the wrong answer
d^2y/dx^x=> 6(6y^5y'+6x(y'*5y^5y'+y^5y''))-10(-y^(-3/2)y'+(1/2)y^(-1/2)y'')+44(y'y'+2yy'')
Thanks for the help
You are (almost) correct on the y' calculation. For the actual calculation of y' you didn't do the exponentiation in formula but did do it in the calculation so that it turned out correct. ThusUse implicit differentiation to find the second derivative at point (9,1) is y is given the function: 6 x y^6 - 10 y^(1/2) = 44 y^2
Help much welcomed
6y^6+36xy^5y'-5y-1/2y'=88yy'
which leads to
6 y6 + y' (36 x y5 - 88y - 5y-1/2) = 0
You should probably do the second derivative from that equation as you seemed to have messed it up in the other form.
Cool thanks, so from
6 y6 + y' (36 x y5 - 88y - 5y-1/2) = 0
I did the second derivative and got
36y^(5)y' +y''(36y^(5)+180xy^(4)y'-88y'+((5)/(2))y^(((-3)/(2)))y')=0
= 36y^(5)y'+36y^(5)y''+180xy^(4)y'y''-88y'y''+((5)/(2))y^(((-3)/(2)))y'y''
is this correct?
6 y6 + y' (36 x y5 - 88y - 5y-1/2) = 0
I did the second derivative and got
36y^(5)y' +y''(36y^(5)+180xy^(4)y'-88y'+((5)/(2))y^(((-3)/(2)))y')=0
= 36y^(5)y'+36y^(5)y''+180xy^(4)y'y''-88y'y''+((5)/(2))y^(((-3)/(2)))y'y''
is this correct?