How it is equal to (del f)/(del x′)=(del f)/(del x)cos theta+(del f)/(del y)sin theta Can you explain?



Answered question


There are given equations,
x = x cos θ y sin θ y = x sin θ + y cos θ
f x = f x x x + f y y x
I don't understand how it is equal to
f x = f x cos θ + f y sin θ
Can you explain?

Answer & Explanation



Beginner2022-09-15Added 14 answers

x and y are functions that depend on x′ and y′, i.e.,
x ( x , y ) = x cos θ y sin θ , y ( x , y ) = x sin θ + y cos θ .
x x = x ( x cos θ y sin θ ) = x ( x cos θ ) = cos θ .
Similarly, y x = sin θ .

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