how to differentiate and plot of this function

k1= @(x)  sqrt(1-x^2);
k2=@(x)  sqrt(2-x^2);
k3=@(x)  sqrt(3-x^2);
k4=@(x)   sqrt(4-x^2);
r1=@(x) (k1-k2)/(k1+k2);
r2=@(x) (k3-k4)/(k3+k4);
r3= @(x) (k2-k3)/(k2+k3);
y=@(x,d2,d3)  -2*atan(1i*(1-r1)/(1+r1))*exp((1-r2*k1*d2)/(1+r2*km*d2))--2*atan(1i*(1-r3)/(1+r3))*exp((1-k2*d3)/(1+r4*k2*d3));

how to calculate dy/dx dy/dd2 and dy/dd3

plot d2 vs dy/dd2/dy/dd3

variation of d2 from 1 to 100;

y is multivariable depending upon d2,d3 x

[KSSV]

Did you try to run the code and see?

r1=(k1-k2)/(k1+k2);

What is d2 and d3?

Answer 1

[Hiro]

Why don't you use symbolic math expressions as follows?

Please run the script below:

syms k1(x) k2(x) k3(x) k4(x) r1(x) r2(x) r3(x) y(x,d2,d3)

k1 = sqrt(1-x^2)

k1 = 

k2 = sqrt(2-x^2)

k2 = 

k3 = sqrt(3-x^2)

k3 = 

k4 = sqrt(4-x^2)

k4 = 

r1 = (k1-k1)/(k1+k2)

r1 = 

0

r2 = (k3-k4)/(k3+k4)

r2 = 

r3 = (k2-k3)/(k2+k3)

r3 = 

Note that the first term (atan) does not work due to its singularity and you've got some typos in the expression and I corrected as follows:

y = -2*atan((1-r1)/(1+r1)) *exp((1-r2*k1*d2)/(1+r2*k1*d2))-2*atan(1i*(1-r3)/(1+r3))*exp((1-k2*d3)/(1+r3*k2*d3))

y = 

dydx = diff(y,x)

dydx = 

dydd3 = diff(y,d2)

dydd3 = 

dydd4 = diff(y,d3)

dydd4 = 

[shiv gaur]

is there any method with out syms pl plot the solve equation

[Hiro]

I don't think what you want to do is solve anything. I suppose you want to derive the partial derivatives.

Iif you want to get the analytic forms of the derivatives, use Symbolic Math otherwise numerical derivative would be a good fit.

The easiest way to use numerical derivative is use "approximation" such as numerical derivatives - you can chop the variables into small intervals and perform the calculations as shown in the document.