Use logarithmic differentiation to find the derivative

[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 ?

 

[Mark44]

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 ?

In your 4th line you have a mistake.
Your 3rd line is:
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.

 

[SammyS]

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 ?

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.

 

[Bipolarity]

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

BiP

 

[manal950]

thanks so much ...

 

[manal950]

can check this answer please

 

[SammyS]

can check this answer please

You really should start a new thread for this.

The 1/3 multiplies both logarithms .

 

[manal950]

thansk