What is the first differential of #y= e^sinsqrtx# ?

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Answer 1 · 2017-01-07T05:22:25

#dy/dx=(e^(sin(sqrtx))*cos(sqrtx))/(2sqrtx)#

#y= e^sinsqrtx#

Applying the chain rule:

#dy/dx=e^(sin(sqrtx)) * d/dx(sin(sqrtx))#

Applying the chain rule again:

#dy/dx=e^(sin(sqrtx)) * cos(sqrtx) * d/dx(sqrtx)#

Applying the power rule:

#dy/dx=e^(sin(sqrtx)) * cos(sqrtx) * 1/2x^(-1/2)#

#dy/dx=(e^(sin(sqrtx))*cos(sqrtx))/(2sqrtx)#