Question

Find the derivative of y w.rt. x.
2x
.-1sxsi
1+x
1. y = sin​

Answer 1

Answer:

Step-by-step explanation:

y=(sinx)  

cos  

−1

x

 

Taking log on both sides  

logy=cos  

−1

x.log(sinx)

Differentiating w.r.t x,  

y

1

​  

(  

dx

dy

​  

)=cos  

−1

x.  

dx

d

​  

[log(sinx)]+log(sinx)  

dx

d

​  

(cos  

−1

x)

=cos  

−1

x.[  

sinx

1

​  

.cosx]+log(sinx).[  

1−x  

2

 

​  

 

−1

​  

]

y

1

​  

(  

dx

dy

​  

)=cos  

−1

x.cotx+log(sinx)[  

1−x  

2

 

​  

 

−1

​  

]

[∵  

dx

d

​  

(logx)=  

x

1

​  

 

dx

d

​  

cos  

−1

x=  

1−x  

2

 

​  

 

−1

​  

]

∴  

dx

dy

​  

=y[cos  

−1

x.cotx+log(sinx).[  

1−x  

2

 

​  

 

−1

​  

]]  

dx

dy

​  

=(sinx)  

cos  

−1

x

[cos  

−1

x.cotx−  

1−x  

2

 

​  

 

log(sinx)

​