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How do you differentiate #f(x)=x/(2^sqrt(x-3))# using the chain rule?

1 Answer

Nov 1, 2016

#f'(x)=(2^(sqrt(x-3))-1/2(xln2) 2^(sqrt(x-3)) (x-3)^(-1/2))/(2^(sqrt(x-3)))^2#

Explanation:

#f(x)=x/2^(sqrt(x-3))#

Use quotient rule and chain rule

#f=x,# #g=2^(sqrt(x-3))=2^((x-3)^(1/2))#

#f'=1,# #g'=2^((x-3)^(1/2)) ln 2 *1/2(x-3)^(-1/2)*1 #

#f'(x)=(2^(sqrt(x-3))-1/2(xln2) 2^(sqrt(x-3)) (x-3)^(-1/2))/(2^(sqrt(x-3)))^2#

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