What is the derivative of tan(xy)?

1 Answer
May 30, 2016

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