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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?

2 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 $$x$$? Staff · 2 months, 2 weeks ago