If I had the derivative of an equation and had data points how would I plot them

My derivative is 1 - (sin(x))/(2√(x)) - (√x)(cos(x)) and x = [1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0] how would I plot them?

Answer 1

[Torsten]

d = @(x)1 - sin(x)./(2*sqrt(x)) - sqrt(x).*cos(x);
x  = [1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0];
plot(x,d(x))

[Batuhan Yildiz]

Two Questions:

1. why add the @(x)?
2. would this code also work?

x=[1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0] ;
y=x-sqrt(x).*sin(x);
dy=diff(y)./diff(x);
plot(x(2:end),dy);

[Torsten]

why add the @(x)?

I defined the derivative d as a function. Alternatively, you can of course use

x  = [1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0];
d = 1 - sin(x)./(2*sqrt(x)) - sqrt(x).*cos(x);
plot(x,d)

would this code also work?

If you are too lazy to compute the exact derivative, you can use the approximation

dy = diff(y)./diff(x)

formed by finite difference quotients.

But note that d gives you an approximate derivative in points (x(1:end-1)+x(2:end))/2, not in x(2:end). Thus for the plot you should use

plot((x(1:end-1)+x(2:end))/2,dy)

instead of

plot(x(2:end),dy)

Alternatively, you can compute the derivative symbolically:

syms x 
y = x-sqrt(x).*sin(x);
dy = diff(y,x)

dy = 

Answer 2

[Walter Roberson]

if you have numeric derivative and you want to plot the original curve (to within a constant shift) then use cumtrapz() and plot that.