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Let f(x)=e^(x),g(x)={:{(x^(2),if,xlt(1)/(2)),(x-(1)/(4),if,xge(1)/(2)):} and h(x)=f(g(x)). The derivative of h(x) and x=(1)/(2) is e^((1)/(a)) then a equal to

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Solution :`h(X)={{:(e^(x^(2)),XLT(1)/(2)),(e^((x-(1)/(4))),XGE(1)/(2)):}`
`h((1)/(2))=h(((1)/(2))^(+))=h(((1)/(2))^(-))=e^((1)/(4))`
`impliesh^(')((1)/(2))=e^((1)/(4)),a=4`


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