How do you differentiate # y =- ln( x^2 - x +4) # using the chain rule?

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Answer 1 · 2016-02-07T21:20:46

#y'=(1-2x)/(x^2-x+4)#

The chain rule, in the case of a natural logarithm function, shows that

#d/dx[ln(f(x))]=1/f(x)*f'(x)#

Applying this to the current question, we see that

#y'=-1/(x^2-x+4)*d/dx[x^2-x+4]#

The derivative can be found through the power rule.

#y'=-1/(x^2-x+4)*(2x-1)#

Simplified, this yields

#y'=(1-2x)/(x^2-x+4)#