The given function can be rewritten as:
and so the form of the chain rule that applies here is:
d
dx |
u-2 |
= |
-2u-3 |
du
dx |
Therefore,
d
dx |
4(x2 + x)-2 |
= | 4(-2)(x2 + x)-3 |
d
dx |
(x2 + x) |
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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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