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Help: understanding partial derivative

We are given \(x = r\cos \theta\) and \(y = r\sin \theta\). Find partial derivative of 'r' w.r.t 'x'.
I tried solving this way
\(r = x\sec \theta\).
\(\frac{dr}{dx}\) = \(\sec \theta\). [ I have used the symbol 'd' for partial derivative].
Also,squaring and adding both equations in question we get,
\(r^2 = x^2 + y^2\).
\(2r\frac{dr}{dx} = 2x\).
\(\frac{dr}{dx} = \frac{x}{r}\).
\(\frac{dr}{dx} = \frac{r\cos \theta}{r}\) [As given, \(x=r\cos \theta\)].
= \(\cos \theta\).
I got two different answers I am confused where am i wrong?

Note by Sonveer Yadav
8 months, 2 weeks ago

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Do you know what a partial derivative is?

Did you apply the product rule correctly?

Hint: Does \( \theta \) depend on \(x\)? Calvin Lin Staff · 8 months, 2 weeks ago

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