How to apply the chain rule to a double partial derivative of a multivariable function? f(x,y)=e^(xy) g(x,y)=f (sin(x^2+y),x^2+2y+1 Let’s compute d^2g/dx^2(0,0)

2k1ablakrh0 2022-09-24 Answered
How to apply the chain rule to a double partial derivative of a multivariable function?
f ( x , y ) = e x y g ( x , y ) = f ( sin ( x 2 + y ) , x 3 + 2 y + 1 )
Let’s compute 2 g x 2 ( 0 , 0 )
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Answers (1)

xjiaminhoxy4
Answered 2022-09-25 Author has 9 answers
If we let f be defined as f ( u , v ) = e u v instead, for clarity, then
g x = f u u x + f v v x
Once you've calculated the first partial derivative, you repeat the above on said partial derivative to get the second derivative.
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