Use logarithmic differentiation to find the derivative

1. Dec 13, 2012

manal950

Hi ..

Use logarithmic differentiation to find the derivative

can please check my answer and How I can know if the question want answer by using logarithmic differentiation or not ?

2. Dec 14, 2012

Staff: Mentor

In your 4th line you have a mistake.
ln y = (1/2) ln(x2 + x)

When you differentiate the left side, you should get (1/y) y', due to the chain rule.

In your last line a factor of y seems to have magically popped up on the right side. You got the right value for the derivative, but several steps in between are incorrect.

3. Dec 14, 2012

SammyS

Staff Emeritus
Answer is correct, but as Mark pointed out there are some errors along the way.

It could be simplified. You have $\ \sqrt{x^2+x}\$ in the numerator and x2 + x in the denominator.

If you have x in an exponent and also have x in the base, then logarithmic differentiation can be helpful.

The function you are differentiating here can be done more easily by simply applying the chain rule.

4. Dec 14, 2012

Bipolarity

You usually use logarithmic differentiation when the exponent is also a variable.

BiP

5. Dec 14, 2012

manal950

thanks so much ...

6. Dec 14, 2012

manal950

7. Dec 14, 2012

SammyS

Staff Emeritus
You really should start a new thread for this.

The 1/3 multiplies both logarithms .

8. Dec 14, 2012

thansk