<p>Does anyone know how to find the 4th derivative of xlnx?</p>
<p>Use the product rule to get the first derivative, which is lnx +1.</p>
<p>Then take the derivative of lnx, which is 1/x, and add it to the derivative of 1, which is 0, so that the second derivative is 1/x, or x^-1.</p>
<p>Then use the chain rule, and get -1x^-2 as your third derivative.</p>
<p>Use the chain rule again to find the fourth derivative and get 2x^-4, which simplifies to 2x/x^4, which again simplifies to 2/x^3.</p>
<p>I don't think u should get 2x^-4 at any point in the problem...</p>
<p>Do you mean the power rule hatchamadoo? Your answer is right, but:
Derivative of x^-1 is -1x^-2 by the power rule.
Derivative of -1x^-2 is 2x^-3, or 2/x^3 by the power rule.</p>
<p>I'm not sure where you got 2x^-4, but that simplifies to 2/x^4, not 2x/x^4.</p>
<p>f(x) = xlnx</p>
<p>f'(x) = x(1/x) + lnx = 1 + lnx</p>
<p>f"(x) = 1/x</p>
<p>f'"(x) = -x^-2</p>
<p>f""(x) = 2x^-3 or 2/x^3</p>
<p>thank you guys</p>
<p>In my class we call it the chain rule, which is essentially just another name for the power rule.</p>
<p>"I'm not sure where you got 2x^-4, but that simplifies to 2/x^4, not 2x/x^4."</p>
<p>Oops, thats what I meant, sorry.</p>
<p>But the chain rule is entirely different. Unless you are somehow using the chain rule when you use the power rule.</p>
<p>f(x)=xlnx
f'(x)= lnx +1
f"(x)= 1/x
f"'(x)= -1/(x^2)
f(4)(x)=2/(x^3)</p>
<p>i understand that you are calculus, but the exact thing you typed was posted yesterday.</p>
<p>
In my class we call it the chain rule, which is essentially just another name for the power rule.
</p>
<p>That's entirely incorrect. The chain rule is the method of differentiating a composition (i.e. f(g(x)) ), while the power rule is the rule for differentiating x^r.</p>
<p>to find the first derivative, didn't you use the product rule?</p>
<p>then d/dx (ln x) = 1 / x</p>
<p>from there its power rule...</p>
<p>Okay, then I guess I used the power rule, haha.</p>
<p>The way I learned it, the chain rule is used to differentiate factorized polynomials to the power n, where n usually > 1. i.e. (ax + b)^n.
Ive never heard of this power rule. But by saying "x^r" it reminds of differentiating ax^n functions through the rule: nax^n-1.
In conclusion, I guess there are just many different names for the same thing...?</p>
<p>No, there are not. The ax^n rule is the power rule. The chain rule can be used the way you've stated it (because (ax+b)^n is a composition, which could be stated as u^n, where u = ax+b), but it can be used in other instances as well.</p>
<p>My saying x^r was just a different way of saying the power rule.</p>
<p>Here is a good list of the rules: <a href="http://en.wikipedia.org/wiki/Derivative#Rules_for_finding_the_derivative%5B/url%5D">http://en.wikipedia.org/wiki/Derivative#Rules_for_finding_the_derivative</a></p>
<p>Look, chain rule is the equivalent of PEMDAS in arithmetic. Thats all it is.</p>
<p>Chain Rule is to Derrivative as PEMDAS is to Arithmetic.</p>