Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

what would be the answer in this calculus problem?

Find fx, fy, and fz

f(x,y,z) = 5z ln (x^3 y^5 cos 3z)

fx = ???

fy = ???

fz = ???

Attachment image

1 Answer

Relevance
  • Alan
    Lv 7
    4 months ago

    Using the chain rule 

    f_x =  (3x^2 )5z/ |(x^3y^5 cos(3z) |

    f_x  =   15z / |(xy^5 (cos(3z) )|  Using the chain rule f_y=      5z*(5y^4) / |(x^3y^5 cos(3z) )|  = 25z/ |(x^3y cos(3z) )|   f_z   =  d(5z)* ln(x^3y^5 cos(3z)   +   5z * (1 / | x^3 y^5 cos(3z))*(-3sin(3z) ) 

    f_z = 5(ln(x^3y^5 cos(3z) ))-    15z(sin(3z)  /  |  x^3 y^5 cos(3z) |     

    The argument to "ln" must be positive and 

    that is what cause the absolute value to be used.  

    Sometimes you can determine that they are unnecessary 

    but this time I did not determine that yet. 

     

    You may be able to simplify the last one. 

Still have questions? Get your answers by asking now.