# Find dx/dy if y=sin2x

Find $\frac{dx}{dy}$ if $y=\mathrm{sin}2x$
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gwibdaithq
$y=\mathrm{sin}\left(2x\right)$
If you differentiate $\mathrm{sin}\left(x\right)$, you get $\mathrm{cos}\left(x\right).$
So, if you differentiate $\mathrm{sin}\left(u\right)$ you will get $\mathrm{cos}\left(u\right).$
Then let u = 2x.
Since u = 2x, then $\frac{du}{dx}=2.$
And d$\frac{y}{dx}=\left(\frac{dy}{d}u\right)\cdot \left(d\frac{u}{dx}\right).$
Now, $y=\mathrm{sin}\left(u\right)$, with $\frac{dy}{d}u=\mathrm{cos}\left(u\right).$
So, $\frac{dy}{dx}=\left(\frac{dy}{d}u\right)\cdot \left(d\frac{u}{dx}\right)=\mathrm{cos}\left(u\right)\cdot 2$
i.e. $\frac{dy}{dx}=2\mathrm{cos}\left(2x\right)$