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

1 Answer

Jun 1, 2018

#f'(x)=-9/2*((3*x)/(2*x-3))^(-1/2)#

Explanation:

Writing

#f(x)=((3*x)/(2x-3))^(1/2)#

so we get

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

so

#f'(x)=-9/2*((3x)/(2x-3))^(-1/2)#

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