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Question

Differentiate sin-12x+1·3x1+36x with respect to x.

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Solution

We have,
y=sin-12x+1·3x1+36xy=sin-12·6x1+62xput 6x=tanθθ=tan-16xNow,y=sin-12tanθ1+tan2θy=sin-1sin2θy=2θy=2tan-16xdydx=2×16x2×6xlog6dydx=2log66x36x

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