Using chain rule to find the answer?

Question

#(5-(x^2)/2)^3#

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Answer 1 · 2018-03-23T08:09:29

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

Here,

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

We assume that

#y=u^3, # where, #color(blue)(u=5-x^2/2#

#=>(dy)/(du)=3u^2, and (du)/(dx)= 0-(2x)/2=-x#

Applying Chain Rule,

#color(red)((dy)/(dx)=(dy)/(du)*(du)/(dx)#

#:.(dy)/(dx)=3u^2(-x),.....#where,#color(blue)(u=5-x^2/2#

#=>(dy)/(dx)=3color(blue)((5-x^2/2)^2)(-x)#

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