Say x in RR^n and y in RR^n find the explicit expression: (del)/(del y)cos(x^T y)x^T

Bridger Holden

Bridger Holden

Answered question


Solving and verification of : y cos ( x T y ) x T
I am trying to simplify an expression and would like to ask if my approach is correct and also could I simplify this expression further. If so what would I use? I am doing a bit of self-studying here so I must apologize if this is trivial.
Say x R n and y R n find the explicit expression:
y cos ( x T y ) x T
My Answer:
y cos ( x T y ) x T = y sin ( x T y ) x T
Is the answer correct?
Can I simplify this further?

Answer & Explanation



Beginner2022-10-07Added 8 answers

Recall that:
d d y cos ( x y ) = x sin ( x y ) y sin ( x y ) .
Therefore, in your case, the right derivative is:
y cos ( x T y ) x T = x sin ( x T y ) x T
Since sin ( x T y ) is a number, then you can write this as:
y cos ( x T y ) x T = sin ( x T y ) x x T

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