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Answer 1 · 2018-02-05T15:53:41

#dy/dx=1/(2x-3)^(3/2)#

We want to find the derivative of

#y=1/(2x-3)^(1/2)=(2x-3)^(-1/2)#

Use the chain rule #dy/dx=dy/(du)*(du)/dx#

Let #y=u^(-1/2)# and #u=(2x-3)#

Then #dy/(du)=-1/2u^(-3/2)# and #(du)/dx=2#

Apply the chain rule

#dy/dx=-1/2u^(-3/2)*2=-u^(-3/2)#

Substitute #u=(2x-3)#

#dy/dx=-(2x-3)^(-3/2)#

Or

#dy/dx=-1/(2x-3)^(3/2)#