Question

What is the derivative of `tan(xy)`?

Answer 1

`frac{d}{dx}(tan (xy))=\sec ^2(xy)y`

Explanation:

`frac{d}{dx}(tan (xy))`

Applying Chain rule,
`\frac{df(u)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}`

Let `xy=u`

`=\frac{d}{du}(\tan (u))\frac{d}{dx}(xy)`

We know,
`\frac{d}{du}(\tan (u))=\sec ^2(u)` and,
`\frac{d}{dx}(xy)=y`

So,
`=\sec ^2(u)y`

Finally,substituting back,`xy=u`
`=\sec ^2(xy)y`