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

Gaintentavyw4 2022-09-14 Answered
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?
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Answers (1)

ignaciopastorp6
Answered 2022-09-15 Author has 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 .
So
x x = x ( x cos θ y sin θ ) = x ( x cos θ ) = cos θ .
Similarly, y x = sin θ .

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