Use Equation to find \frac{dy}{dx} \tan^{-1}(x^2y)=x+xy^2

gabioskay7

gabioskay7

Answered question

2021-11-15

Use Equation to find dydx
tan1(x2y)=x+xy2

Answer & Explanation

May Dunn

May Dunn

Beginner2021-11-16Added 12 answers

tan1(x2y)=x+xy2
tan1(x2y)xxy2=0
F(x,y)=tan1(x2y)xxy2=0
Suppose that an equation F(x,y)=0 defines y Implicity as a differentiable function of x.
Then
dydx=FxFy
Fx=11+(x2y)2×(2xy)1y2
Fx=2xy1+x4y21y2
Fx=2xy(1+y2)(1+x4y2)1+x4y2
Fy=x21+(x2y)22xy
Fy=x22xy(1+x4y2)1+x4y2
Therefore,
dydx=FxFy=2xy(1+y2)(1+x4y2)1+x4y2x22xy(1+x4y2)1+x4y2=(1+y2)(1+x4y2)2xyx22xy(1+x4y2)
Result:

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