Tangent line to a curve at a given point

https://www.mathworks.com/matlabcentral/answers/89306-tangent-line-to-a-curve-at-a-given-point

 

 

 

%Example
t=0:0.01:10
y=sin(t)
plot(t,y)
%-------------------------
dy=diff(y)./diff(t)
k=220; % point number 220
tang=(t-t(k))*dy(k)+y(k)
hold on
plot(t,tang)
scatter(t(k),y(k))
hold off

 

 

 

 

gradient(y,t) is better than diff(y)/diff(t), because it applies a 2nd order method. At least this is true for numerical differentiation. Does this concern symbolic operations also? I cannot test this, because I do not have the symbolic toolbox.