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Question
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Solution
y = `sin(tan(sqrt(sinx)))`
y = f(g(x))
`("d"y)/("d"x)` = f'(g(x)) . g'(x)
`("d"y)/("d"x) = cos(tan(sqrt(sinx))) sec^2(sqrt(sinx)) xx 1/2(sinx)^(1/2 - 1) cos x`
`("d"y)/("d"x) = 1/2 cos (tan(sqrt(sinx))) sec^2 (sqrt(sinx)) (sinx)^(- 1/2) cosx`
`("d"y)/("d"x) = (cos(tan(sqrt(sinx))) sec^2(sqrt(sinx)) cosx)/(2(sinx)^(1/2)`
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