partial differential for nonlinear equation

i want the partial differential of this equation w.r.t X , Y and Z

31.65951=sqrt((20460991.052399-X)^2+(11012393.207537-Y)^2+(13140061.841029-Z)^2)-sqrt((20462649.31-X)^2+(11012196.356-Y)^2+(13137623.266-Z)^2)

Answer 1

[Mischa Kim]

Use gradient

 syms X Y Z
 Eq = -31.65951 + sqrt((20460991.052399-X)^2+(11012393.207537-Y)^2+(13140061.841029-Z)^2)-sqrt((20462649.31-  X)^2+(11012196.356-Y)^2+(13137623.266-Z)^2);
 gradient(Eq)
 ans =
 (2*X - 5492455463362645/134217728)/(2*((Z - 3527258492164819/268435456)^2 + (X - 5492455463362645/268435456)^2 + (Y - 2956116792316497/268435456)^2)^(1/2)) - (2*X - 5492900598497935/134217728)/(2*((Z - 7053207784329839/536870912)^2 + (X - 5492900598497935/268435456)^2 + (Y - 5912127900768797/536870912)^2)^(1/2))
 (2*Y - 2956116792316497/134217728)/(2*((Z - 3527258492164819/268435456)^2 + (X - 5492455463362645/268435456)^2 + (Y - 2956116792316497/268435456)^2)^(1/2)) - (2*Y - 5912127900768797/268435456)/(2*((Z - 7053207784329839/536870912)^2 + (X - 5492900598497935/268435456)^2 + (Y - 5912127900768797/536870912)^2)^(1/2))
 (2*Z - 3527258492164819/134217728)/(2*((Z - 3527258492164819/268435456)^2 + (X - 5492455463362645/268435456)^2 + (Y - 2956116792316497/268435456)^2)^(1/2)) - (2*Z - 7053207784329839/268435456)/(2*((Z - 7053207784329839/536870912)^2 + (X - 5492900598497935/268435456)^2 + (Y - 5912127900768797/536870912)^2)^(1/2))

[ahmed ashiry]

error

syms X Y Z Eq = -31.65951 + sqrt((20460991.052399-X)^2+(11012393.207537-Y)^2+(13140061.841029-Z)^2)-sqrt((20462649.31- X)^2+(11012196.356-Y)^2+(13137623.266-Z)^2); gradient(Eq) ??? Error using ==> zeros Trailing string input must be a valid numeric class name.

Error in ==> gradient at 64 g = zeros(size(f),class(f)); % case of singleton dimension

[Mischa Kim]

Ahmed, how are you running these lines of code? Within a script/function?

Can you get it to run in the MATLAB command window?

[ahmed ashiry]

thanks for your reply > but i want the version of you matlab to solve the above function gradient