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Turiski
Lv 6
Turiski asked in Science & MathematicsMathematics · 1 decade ago

What is d(f(x,y))/d(x^2)?

I know that I need partial differentiation to do this, and I was trying to do it with the limit process, but I can't figure out how to set it up.

I need it for two problems:

f(x,y) = xy(y+1) [or x(y^2)+xy] and

f(x,y) = sinxy

Note: I'm not looking for the second derivative. That would be (d^2)f/d(x^2).

1 Answer

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  • Michael E
    Lv 7
    1 decade ago
    Favourite answer

    Let z = x^2 and

    so dz/dx=2x and dx/dz=1/(2x)

    df/d(x^2) = df/dz = y(y+1) dx/dz = y(y+1) / 2x

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