Derivative

[ozgunatalay]

Help me

URL=http://www.yukle.tc]

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[Deleted member 4993]

Help me

URL=http://www.yukle.tc]

[/URL]

We will - as soon as you show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[ozgunatalay]

I'm on both sides of the equation in the function "ln" After the shock, while the derivative of the function difficult. There are a lot of action, and that I will distribute my attention.

Sorry for my bad english. =)

 

[Deleted member 4993]

I'm on both sides of the equation in the function "ln" After the shock, while the derivative of the function difficult. There are a lot of action, and that I will distribute my attention.

Sorry for my bad english. =)

\(\displaystyle y = \frac{(x^2+2)^{\frac{3}{2}}\cdot (x^2+9)^{\frac{4}{9}}}{(x^3+6x)^{\frac{4}{11}}}\)

Where is "ln" coming from?

 

[ozgunatalay]

I've solved the question but i'm not sure, It s correct or not

 

[Deleted member 4993]

I've solved the question. But my answer is correct I'm not sure. I'll send the solution.

[/URL]

Looks good to me....

Now I understand what you meant by "ln" both sides.

 

[ozgunatalay]

You or other friends, not contented with just looking, if you solve the problem and if you share the correct answer here, and I'll be more useful for me and for yourself.

 

[BigGlenntheHeavy]

On occasion, it is convenient to use logarithms as an aid in differentiating nonlogarithmic functions. We call this procedure logarithmic differentiation, and the above example fits the bill, to wit:

\(\displaystyle y = \ \frac{(x^{2}+2)^{3/2}(x^{2}+9)^{4/9}}{(x^{3}+6x)^{4/11}}\)

\(\displaystyle Hence, \ ln|y| \ = \ ln\bigg[\frac{(x^{2}+2)^{3/2}(x^{2}+9)^{4/9}}{(x^{3}+6x)^{4/11}}\bigg]\)

\(\displaystyle ln|y| \ = \ \frac{3}{2}ln(x^{2}+2)+\frac{4}{9}ln(x^{2}+9)-\frac{4}{11}ln(x^{3}+6x)\)

\(\displaystyle \frac{y'}{y} \ = \ \frac{3x}{x^{2}+2}+\frac{8x}{9(x^{2}+9)}-\frac{4(3x^{2}+6)}{11(x^{3}+6x)}\)

\(\displaystyle Hence \ y' \ = \ y\bigg[\frac{3x}{x^{2}+2}+\frac{8x}{9(x^{2}+9)}-\frac{4(3x^{2}+6)}{11(x^{3}+6x)}\bigg]\)

\(\displaystyle I'll \ quit \ here.\)

 

[ozgunatalay]

Thank you for your solution