What is #f_x# when #f (x,y) = sin^2 (x^2y^2)# ?

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Answer 1 · 2018-04-02T05:32:38

# rArr f_x=(delf)/(delx)=2xy^2sin(2x^2y^2)#.

#f(x,y)=sin^2(x^2y^2)=[sin{(xy)^2}]^2#.

Recall that, # f_x," denoted also as "(delf)/(delx)",# is the derivative of #f#

w.r.t. #x,# treating #y,# as constant.

Accordingly, #f_x=2sin{(xy)^2}*del/(delx)[sin{(xy)^2}]#,

#=2sin(x^2y^2)*cos{(xy)^2}*del/(delx)(xy)^2#,

#=color(red)(2sin(x^2y^2)cos(x^2y^2))*del/(delx)(x^2y^2)#,

#=color(red)(sin(2x^2y^2))*{y^2del/(delx)(x^2)}....[because, y" is constant]"#,

#=sin(2x^2y^2){y^2*2x}#.

# rArr f_x=(delf)/(delx)=2xy^2sin(2x^2y^2)#.

Enjoy Maths.!