How do you use the chain rule to differentiate #y=3/(5x^2-4)#?

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Answer 1 · 2018-03-25T12:10:43

#(dy)/(dx)=-(30x)/(5x^2-4)^2#

Here,

#y=3/(5x^2-4)#

Substituting , #y=3/u, and u=5x^2-4#

#(dy)/(du)=-3/u^2 and (du)/(dx)=10x#

Using Chain Rule,

#(dy)/(dx)=(dy)/(du)(du)/(dx)#

#=>(dy)/(dx)=(-3/u^2)(10x)#

Substituting back, #u=5x^2-4#

#(dy)/(dx)=-3/(5x^2-4)^2xx10x#

#=-(30x)/(5x^2-4)^2#