The given function can be rewritten as:

and so the form of the chain rule that applies here is:

Therefore,


Using the Verbal Form of the Chain Rule

The verbal form of the chain rule above states:

The derivative of a quantity to the -2 is -2 times that (original) quantity to the -3, times the derivative of the quantity.
The derivative of (x2 + x) to the -2 is -2 times (x2 + x) to the -3, times the derivative of (x2 + x).

That is,

The derivative of (x2 + x) to the -2 is -2 times (x2 + x) to the -3, times (2x + 1)..

If you now write this in symbols, you get the same answer as above.


Enter the answer as -8*(x^2+x)^(-3)*(2*x+1) or -8*(2*x+1)/(x^2+x)^3


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