How to define second derivative in symbolic

AA, I have a project to derive some equations that defined in symbolic variables. For example, r= cos(A), I want the symbolic system show me a result that dr/dA = -sin(A)*(dA/d) as A has derivatives values dA/d and so far for d²A/d² If I want the second derivative of r.

Answer 1

[Star Strider]

Use the symbolic diff function —

syms A 
r(A) = cos(A)

r(A) = 

D1r = diff(r)

D1r(A) = 

D2r = diff(r,2)

D2r(A) = 

.

[Anas Zh]

Where is dA/d?

[Star Strider]

Here you go —

syms A(t) 
r = cos(A)

r(t) = 

D1r = diff(r)

D1r(t) = 

D2r = diff(r,2)

D2r(t) = 

Here, A has to be defined as a function of something, otherwise it is treated as a constant. So I made it a function of t.

.

[Mohammed Hamaidi]

That is it

[Star Strider]

Thank you.

[Anas Zh]

Thank you a lot

[Star Strider]

As always, my pleasure!

Answer 2

[Mohammed Hamaidi]

dr/dA = -sin(A)*(dA/d)

d²r/dA² = -cos(A)*(dA/d)^2-sin(A)*d²A/d²

[Anas Zh]

How can I let MATLAB symbolic shows this result as finally, I will substitute the derivative

[Mohammed Hamaidi]

What is A?

[Anas Zh]

 Any variable, it doesn't matter