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

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Answer 1 · 2016-05-30T08:56:57

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

#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#