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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 = ???
1 Answer
- AlanLv 74 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.