Using the Chain Rule Formula

From the table above, we find:

d dx

ln (u)

=

1 u

du dx

Therefore,

d dx	ln( x2+2x1)	=	1 x2+2x1	d dx	(x2+2x1)
		=	1 x2+2x1	(2x+2)
		=	2(x+1) x2+2x1

Using the Verbal Form of the Chain Rule

The verbal form of the chain rule above states:

The derivative of the natural logarithm of a quantity is the reciprocal of that (original) quantity, times the derivative of that quantity.

The derivative of the natural logarithm of (x²+2x1) is the reciprocal of (x²+2x1), times the derivative of (x²+2x1).

That is,

The derivative of the natural logarithm of (x²+2x1) is the reciprocal of (x²+2x1), times (2x+2).

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

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