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