Math Is Fun Forum

katyperryrocksmycar

Guest

calculus like problem

problem is first
x(10-4lnx)
i think that comes out to
10x-4xlnx right?

next i need to find the derivative
i thnk rthats
d/dx(10x)-[d/dx(4x)(lnx)+(10x)d/dx(lnx)
which is 10-4lnx?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: calculus like problem

Hi katyperryrocksmycar;

x(10-4lnx)
i think that comes out to 10x-4xlnx right?

Correct!

The second part is not correct. Check your work please.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

katyperryrocksmycar

Guest

Re: calculus like problem

is it
d/dx(8x)-d/dx(2xlnx?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: calculus like problem

Hi katyperryrocksmycar;

That is not quite right either. Perhaps if I saw some of your work...

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

henryhightower

Guest

Re: calculus like problem

So since f(x)=10x-4xlnx is correct,
f'(x)= d/dx(10x)-d/dx(4xlnx)
      = 10(1)-4d/dx(xlnx)
      = 10 - 4(x*1/x)
      = 10 - 4(1)
      = 6?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: calculus like problem

Hi;

The error is right here. In your 2nd to 3rd line.

10 - 4(x*1/x)

The 10 is correct of course but that is not how you differentiate -4x ln(x). ( Hint, you already know how to differentiate a product of 2 functions. You do not just multiply the derivatives of the 2 functions.)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

henryhightower

Guest

Re: calculus like problem

So it is a combination of rules in there. Then:
=10(1)-d/dx(4xlnx)
=10 - [d/dx(4x)(lnx)+(4x)d/dx(lnx)]
=10 - [(4)(lnx)+4x(1/x)]
=10 - [4lnx + 4]
=10 - 4lnx - 4
=6 - 4lnx?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: calculus like problem

That is correct!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

henryhightower

Guest

Re: calculus like problem

Great! Finally making some headway it seems.

To evaluate f'(x) = 0 in this instance then
f'(x)=0
6 - 4lnx = 0
6 = 4lnx
4lnx = 6
lnx = 6/4
x = e^(6/4)  Looking for the property that backs this part up.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: calculus like problem

Hi henryhightower;

That step is okay because e^x is the inverse operation of ln(x). Loosely put it undoes the ln(x).

That is the correct solution to your equation.

If you want a little more about inverses then go here:

http://www.mathsisfun.com/numbers/inverse.html

http://www.mathsisfun.com/sets/function-inverse.html

http://www.analyzemath.com/inversefunct … ials2.html

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

henryhightower

Guest

Re: calculus like problem

Thanks for your help with the problems tonight Bobbym!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: calculus like problem

Your welcome and welcome to the forum!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.