How do you find the derivative of #h(x)= 1/(6x^2+x+1)^2#?

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Answer 1 · 2016-05-17T16:29:53

#-2(12x+1)/(6x^2+x+1)^3#

This can be done using the chain rule, we have:

#h(x) = 1/(6x^2+x+1)^2#

This can be re written as:

# = (6x^2+x+1)^(-2)#

To apply the chain rule, differentiate the function around the bracket then multiply by the derivative of the function inside the bracket.

#-> h'(x) = d/dx{(6x^2+x+1)^(-2)}=#

#=-2(6x^2+x+1)^(-3)d/dx{6x^2+x+1}#

#=-2(6x^2+x+1)^(-3)(12x+1)#

Which we can write as:

#-2(12x+1)/(6x^2+x+1)^3#

Hence, our final answer.