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Differentiate e^(x)(x^(3) +sqrtx)...

Differentiate ` e^(x)(x^(3) +sqrtx)`

A

`e^(x) { x^(2) +3x^(2) + 1/(2sqrtx) + sqrtx} `

B

`e^(x) { x^(3) +3 + 1/(2sqrtx) + sqrtx} `

C

`e^(x) { x^(3) +3x^(2) + 1/(sqrtx) + sqrtx} `

D

`e^(x) { x^(3) +3x^(2) + 1/(2sqrtx) + sqrtx} `

Text Solution

Verified by Experts

The correct Answer is:
D
`d/(dx) [e^(x)(x^(3) +sqrtx)]= e^(x).d/(dx) (x^(3) +sqrtx) + (x^(3) +sqrtx).d/(dx) (e^(x))`
` e^(x) { 3 x^(2) + 1/2x^(-1//2)} + (x^(3) +sqrtx).e^(x)`
` e^(x) { x^(3) +3x^(2) + 1/(2sqrtx) + sqrtx} `
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