Find y" by implicit differentiation. x^2+4y^2=4

Antinazius 2021-11-17 Answered
Find y" by implicit differentiation.
x2+4y2=4
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Gloria Lusk
Answered 2021-11-18 Author has 18 answers
x2+4y2=4
Differentiate both sides with respect to x
d(x2+4y2)dx=d(4)dx
Remember that the derivative of a constant is 0
d(x2)dx+d(4y2)dx=0
The Chain Rule for differentiation
d[f[g(x)]]dx=d[f[g(x)]]d[g(x)]d[g(x)]fx
2x21+d(4y2)dydydx=0
2x+42y21dydx=0
Subtract 2x from both sides
8ydydx=2x
Divide both sides by 8y
dydx=2x8y=x4y
Differentiate both sides with respect to x
The Quotient Rule for differentiation
ddx[d(x)g(x)]=f(x)g(x)f(x)g(x)[g(x)]2
y=(x)(4y)(x)(4y)(4y)2
y=(1)(4y)(x)(4y)16y2
y=4y+4xy16y2
Substitute y=x
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