Consider the equation y^{3}-\frac{3}{2}x^{2}=1.

Lipossig

Lipossig

Answered question

2021-03-31

Consider the equation y332x2=1.

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-04-02Added 96 answers

Step 1
Consider the equation
y332x2=1
Let us find the second derivative implicitly.
Step 2
Differentiate each term with respect to x
ddx(y332x2)=ddx...(1)
ddx(y3)32ddx(x2)=0
3y2dydx3x=0
dydx=xy2(1)
Step 3
Differentiate second time with respect to x
d2ydx2=ddx(xy2)
=ddx(x)y2ddx(y2x)(y2)2
=1y22ydydxxy4
=y2xdydxy3
Step 4
From equation (1) we have dydx=xy2. Substituting this we get
d2ydx2=y2x(xy2)y3
=y32x2y5
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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