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

1 Answer
Oct 15, 2017

Answer:

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

Explanation:

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:)