Please help with this question:
Obtain F(y) for the function F(x,y) = y^3 sin((y^2)x) ln(4y+x)
Thanks
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)
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)