How do you differentiate #f(x)=e^(secsqrtx)# using the chain rule.?

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Answer 1 · 2015-12-11T00:26:44

#f'(x)=(sec(sqrtx)tan(sqrtx)e^(sec(sqrtx)))/(2sqrtx)#

According to the chain rule,

#f'(x)=e^(secsqrtx)d/dx[secsqrtx]#

First, find the internal derivative (again using the chain rule).

#d/dx[secsqrtx]=secsqrtxtansqrtxd/dx[sqrtx]#

#=1/2x^(-1/2)secsqrtxtansqrtx#

#=(secsqrtxtansqrtx)/(2sqrtx)#

Plug this back in to find #f'(x)#.

#f'(x)=(e^(secsqrtx))(secsqrtxtansqrtx)/(2sqrtx)#

#f'(x)=(sec(sqrtx)tan(sqrtx)e^(sec(sqrtx)))/(2sqrtx)#