maths partial derivatives help?

Please help with this question:

Obtain F(y) for the function F(x,y) = y^3 sin((y^2)x) ln(4y+x)

Thanks :)

Comments

  • Did you mean the partial derivative with respect to y? If so:

    F(x,y) = y^3 (sin (y^2 x) ln (4y+x)

    differentiate with respect to y only treating x as a constant.

    Fy(x,y) = (3y^2) (sin (y^2 x) ln (4y+x) + y^3 cos ((y^2) x) (2yx) ln (4y+x) + y^3 (sin (y^2 x) [ 4/(4y+x)]

    = (3y^2) (sin (y^2 x) ln (4y+x) + 2 xy^4 cos ((y^2) x) ln (4y+x) + 4 y^3 (sin (y^2 x) /(4y+x)

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