Question

differentiate w.r.t.x.
[(tanx)^tanx]^tanx at x=π/4​

Answer 1

Answer:

Consider the following differential eq.

y=((tanx)  

tanx

)  

tanx

&x=  

4

π

​  

 

 

Taking log both side, we get.

logy=tan  

2

xlog(tanx)

 

Differentiate both side w.r.t x, we get.

y

1

​  

 

dx

dy

​  

=2tanxsec  

2

xlog(tanx)+tan  

2

x  

tanx

1

​  

sec  

2

x

y

1

​  

 

dx

dy

​  

=((tanx)  

tanx

)  

tanx

(2tan  

4

π

​  

sec  

2

 

4

π

​  

log(tan  

4

π

​  

)+tan  

4

π

​  

sec  

2

 

4

π

​  

)

dx

dy

​  

=0+2

=2

 

Hence, this is the required answer.