If #f(x)= - e^x # and #g(x) = sqrt(1-x^2 #, how do you differentiate #f(g(x)) # using the chain rule?

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Answer 1 · 2017-07-18T14:12:15

#f'(g(x)) = (xe^(sqrt(1-x^2)))/sqrt(1-x^2)#

#f(x) =-e^x# and #g(x) = sqrt(1-x^2)#

#:. f(g(x)) = -e^(sqrt(1-x^2)#

Applying the chain rule:

#f'(g(x)) = -e^(sqrt(1-x^2))* d/dx (sqrt(1-x^2))#

Applying the chain rule agsin:

#f'(g(x)) = -e^(sqrt(1-x^2))* 1/2 (1-x^2)^(-1/2) * d/dx(1-x^2)#

Applying the chain rule agsin:

#f'(g(x)) = -e^(sqrt(1-x^2))* 1/2 (1-x^2)^(-1/2)* (-2x)#

#= (xe^(sqrt(1-x^2)))/sqrt(1-x^2)#