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प्रश्न
Differentiate the following:
y = `"e"^sqrt(x)`
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उत्तर
y = `"e"^sqrt(x)`
y = `"e"^(x 1/2)`
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
`("d"y)/("d"x) = "e"^(x 1/2) xx "d"/("d"x) (x^(1/2))`
`("d"y)/("d"x) = "e"^sqrt(x) xx 1/2 xx x^(- 1/2)`
`("d"y)/("d"x) = 1/2 "e"^sqrt(x) xx 1/sqrt(x)`
`("d"y)/("d"x) = 1/(2sqrt(x)) "e"^sqrt(x)`
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