Tricky Looking!

1. May 11, 2005

cogs24

y = (4-x) ^ 5x

Just wondering what i should do with this
Thanx

2. May 11, 2005

Jayboy

I guess that depends what the question is. Are you asking for the differential equation to which this is the solution?

Take logs and differentiate for first order ODE?

3. May 12, 2005

cogs24

yes, i have to differentiate it

sorry i didnt specifiy what had to be done, i presumed you knew it was differentiation.

4. May 12, 2005

Jayboy

If it's just finding the derivative then this is probably more a question for the calculus thread.

Anyhoo, i'll do the first part. Take logs to get.

$$ln(y)= 5x ln(4-x)$$

Now differentiate (implicitly on the LHS) and rearrange to get your answer for dy/dx. Have a go and let me know if/where you get stuck.

5. May 12, 2005

cogs24

ok, i understand your instructions, its just a matter of doing the right things now
This is what i got as an answer, unfortunately we arent supplied with answers in this exercise.

following on from your step, this is what i did

1/y * dy/dx = 5 * (1/4-x)
dy/dx = (5/4-x)y
dy/dx = (5/4-x)(4-x)^5x

6. May 12, 2005

dextercioby

Pay attention with the differentiaition of the RHS.It's a product.I'm sure one of the 2 terms will contain the natural logarithm.

Daniel.

7. May 12, 2005

Jayboy

Think with my poor Tex you missed the x after the 5 on the RHS. Take that into account and you're there.

8. May 12, 2005

arildno

Here's another way:
Let $$y(x)=f(u(x),v(x)), f(u,v)=u^{v}, u(x)=4-x, v(x)=5x$$
Then, we have:
$$\frac{dy}{dx}=\frac{\partial{f}}{\partial{u}}\frac{du}{dx}+\frac{\partial{f}}{\partial{v}}\frac{dv}{dx}$$

9. May 13, 2005

cogs24

ahh i see. i didnt spot the product rule on the right, i guess practice makes perfect.
Thanx everyone for the input.

10. May 15, 2005

abia ubong

when differentiating functions of a variable say x raised to another function of xthen lets assume they are T^u,where t and u are fucntions of x,dy/dx =
T^u[du/dx*logt+u(dt/dx)/t]

11. May 15, 2005

abia ubong

when differentiating functions of a variable say x raised to another function of xthen lets assume they are T^u,where t and u are fucntions of x,dy/dx =
T^u[du/dx*logt+u(dt/dx)/t].now let 4-x=t,and u=5x.
take normal procedures and see if it works