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Derivative of sqrte^(sqrt(x)) with re...

Derivative of ` sqrte^(sqrt(x))` with respect to x is

A

` (sqrte^(sqrt(x)))/(2sqrt(xe)^sqrt(x))`

B

` (4e^(sqrt(x)))/(sqrt(xe)^sqrt(x))`

C

` (e^(sqrt(x)))/(4sqrt(xe)^sqrt(x))`

D

` (e^(sqrt(x)))/(sqrt(e)^sqrt(x))`

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` y = (e^(sqrt(x)))^(1//2)`
On differentiating both sides of Eq .(i) w.r.t.x, we get
` (dy)/(dx) = (1)/(2) (e^(sqrt(x)))^((1)/(2)1) (d)/(dx) e^(sqrt(x))`
` rArr (dy)/(dx) = (e^(sqrt(x)))/(2sqrt( e^(sqrt(x))))(d)/(dx) (sqrt(x)) = (1)/(2)(e^(sqrt(x)))/(sqrt(esqrt(x)))xx(1)/(2sqrt(x))`
`rArr = (e^(sqrtx))/(4sqrt(x)sqrt(e^(sqrt(x))))=(e^(sqrt(x)))/(4sqrt(xe^(sqrtx)))` .
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Knowledge Check

  • Derivative of sqrt(e^(sqrtx)) with respect to x is

    A
    `(e^(sqrtx))/(2sqrt(xe^(sqrtx)))`
    B
    `(4e^(sqrtx))/(sqrt(xe^(sqrtx)))`
    C
    `(e^(sqrtx))/(4sqrt(xe^(sqrtx)))`
    D
    `(e^(sqrtx))/(sqrt(e^(sqrtx)))`

  • Derivative of sqrt( tan sqrt(x)) with respect to x is

    A
    `(sec^(2) sqrt(x))/(4sqrt(x)sqrttansqrt(x))`
    B
    `(sec^(2) sqrt(x))/(4sqrt(x)tansqrt(x))`
    C
    `(sec^(2) sqrt(x))/(sqrt(x)sqrttansqrt(x))`
    D
    `(4sec^(2) sqrt(x))/(sqrt(x)sqrttansqrt(x))`

  • The derivative of sqrt(secsqrt(x)) with respect to x , is :

    A
    `(1)/(4sqrt(x))secsqrt(x)tansqrt(x)`
    B
    `(1)/(4sqrt(x))sqrt(secsqrt(x))sinx`
    C
    `(1)/(4sqrt(sqrt(x)))(secsqrt(x))^(3//2)sinsqrt(x)`
    D
    `(1)/(4sqrt(x))secsqrt(x)sinsqrt(x)`

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