Question

y= sec x + 2 cosec x + 5 cot x. find dy/ dx​

Answer 1

y=ln(cosecx−cotx)

Chain rule,

dx

dy

​  

=  

du

dy

​  

⋅  

dx

du

​  

 

Here u=cosecx−cotx

⇒  

dx

dy

​  

=  

cosecx−cotx

1

​  

⋅  

dx

d(cosecx−cotx)

​  

 

⇒  

dx

dy

​  

=  

cosecx−cotx

−cosecx.cotx+cosec  

2

x

​  

 

⇒  

dx

dy

​  

=  

cosecx−cotx

−cosecx(cotx−cosecx)

​  

 

⇒  

dx

dy

​  

=cosecx