How do you differentiate #f(x)=sqrt(1-(3x-3)^2# using the chain rule.?

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Answer 1 · 2017-10-15T15:13:09

The derivative is #color(red)(dy/dx=-(9(x-1))/sqrt(1-(3x-3)^2))#

Let the function given be #y# such that,

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

Now, it is better to simplify the term #(1-(3x-3)^2)#.

#:.y=sqrt(1-9(x-1)^2)#

#:.y=sqrt(1-9(x^2-2x+1)#

#:.y=sqrt(1-9x^2+18x-9)#

#:.y=sqrt(-9x^2+18x-8)#

#:.y=(-9x^2+18x-8)^(1/2)#

Now differentiating w.r.t #x# we get,

#dy/dx=1/2cdot(-9x^2+18x-8)^(1/2-1)xxd/dx(-9x^2+18x-8)#

#:.dy/dx=1/(2sqrt(-9x^2+18x-8))xx(-18x+18-0)#

Now, simplifying the equation #rarr#

#:.dy/dx=-18/(2sqrt(1-(3x-3)^2))xx(x-1)#

#:.color(red)(dy/dx=-(9(x-1))/sqrt(1-(3x-3)^2))#. (Answer)

Hope it Helps:)