Finding the gradient of the function

I need to find the gradient (differentiation) of the below function k1 wrt a11 for the values of z1 and plot with respect a11.

z1 = [0.00008 0.009]';
a11 = -2:0.002:2;
k1 = atan(((0.02 + a11)./z1)) + atan((0.03 - a11)./z1);

[DGM]

Edited to restore deleted question.

Answer 1

[Star Strider]

Symbolically —

syms a11 z1 
sympref('AbbreviateOutput',false);
k1 = atan(((0.02 + a11)./z1)) + atan((0.03 - a11)./z1)

k1 = 

grad_k1 = gradient(k1)

grad_k1 = 

grad_k1_fcn = matlabFunction(grad_k1)

grad_k1_fcn = function_handle with value:
    @(a11,z1)[1.0./(z1.*(1.0./z1.^2.*(a11+1.0./5.0e+1).^2+1.0))-1.0./(z1.*(1.0./z1.^2.*(a11-3.0./1.0e+2).^2+1.0));-(1.0./z1.^2.*(a11+1.0./5.0e+1))./(1.0./z1.^2.*(a11+1.0./5.0e+1).^2+1.0)+(1.0./z1.^2.*(a11-3.0./1.0e+2))./(1.0./z1.^2.*(a11-3.0./1.0e+2).^2+1.0)]

.

[Amy Topaz]

Could you plot and show me the plot please

[Star Strider]

Sure!

syms a11 z1 
sympref('AbbreviateOutput',false);
k1 = atan(((0.02 + a11)./z1)) + atan((0.03 - a11)./z1)

k1 = 

grad_k1 = gradient(k1)

grad_k1 = 

grad_k1_fcn = matlabFunction(grad_k1)

grad_k1_fcn = function_handle with value:
    @(a11,z1)[1.0./(z1.*(1.0./z1.^2.*(a11+1.0./5.0e+1).^2+1.0))-1.0./(z1.*(1.0./z1.^2.*(a11-3.0./1.0e+2).^2+1.0));-(1.0./z1.^2.*(a11+1.0./5.0e+1))./(1.0./z1.^2.*(a11+1.0./5.0e+1).^2+1.0)+(1.0./z1.^2.*(a11-3.0./1.0e+2))./(1.0./z1.^2.*(a11-3.0./1.0e+2).^2+1.0)]

figure
hfs = fsurf(grad_k1, [-1 1  -1 1]*4, 'MeshDensity',75);
hfs(1).EdgeColor = 'interp';                                % Optional
hfs(2).EdgeColor = 'interp';                                % Optional

EDIT — (14 Apr 2022 at 13:22)

Changed (increased) 'MeshDensity'.

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