Question

DIFFERENTIATE (sin-1 x)^x w.r.t. (sin x)^tan x
please help​

Answer 1

Answer

let y=sin(tan  

−1

e  

x

)

now, take differentiation on both side wrt x get

1−y  

2

 

​

 

1

​

 

dx

dy

​

=  

1+(e  

−x

)  

2

 

1

​

.  

dx

d

​

(e  

−x

)

dx

dy

​

=  

1−y  

2

 

​

×  

1+e  

−2x

 

1

​

.(−e  

−x

)

so,  

dx

dy

​

=−  

1+e  

−2x

 

1−sin  

2

(tan  

−1

e  

−x

)

​

 

​

 

​

×e  

−x

 

or,  

dx

dy

​

=−  

1+e  

−2x

 

cos(tan  

−1

e  

−x

)

​

 

​

x  

e  

−x