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प्रश्न
Differentiate the following with respect to x.
`sqrtx + 1/root(3)(x) + e^x`
उत्तर
Let y = `sqrtx + 1/root(3)(x) + e^x`
y = `x^(1/2) + x^(1/3) + e^x`
`[because 1/root(3)(x) = 1/(x^(1/3)) = x^(1/3)]`
`"dy"/"dx" = "d"/"dx" (x^(1/2)) + "d"/"dx" (x^(-1/3)) + "d"/"dx" (e^x)`
`= 1/2 x^(1/2 - 1) + ((- 1)/3) x^((-1)/3 - 1) + e^x`
`= 1/2 x^((-1)/2) - 1/3 1/(x^(4/3)) + e^x`
`= 1/2 1/(x^(1/2)) - 1/3 1/(x^(4/3)) + e^x`
`= 1/(2sqrtx) - 1/(3 root(3)(x^4)) + e^x`
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