Differentiate the following functions with respect to `tan5x^@`

Explanation

Let `y=tan 5 x^circ`

`Rightarrow y=tan (5 x times pi/180)`

Differentiate it with respect to `x` we get,

`(d y)/(d x)=d/(d x) tan (5 x times pi/180)`

`=sec ^2(5 x times pi/180) d/(d x) (5 x times pi/180) text [ using chain rule ]`

`=(5 pi/180) sec ^2(5 x times pi180)`

`=(5 pi)/(180) sec ^2(5 x^circ) `

Hence, `d/(dx) (tan 5 x^circ)=(5 pi)/(180) sec ^2(5 x^circ)`