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`