Thread: Differentiation Question

So I've been trying to differentiate this one problem, and then solve when the derivative is equal to 2. The equation in question is sqrt[(5x+1)/(4x^2+1)

Now for my answer before plugging in two I got .5((((20x^2+5)-(40x^2+8x))/(16x^4+8x^2+1))^(-1/2)

however this is obviously not a correct calculation - what was I doing wrong?

This site helped me alot.

http://www.mathhelpforum.com/math-he...step-step.html
solving derivatives step-by-step

Just type in sqrt[(5x+1)/(4x^2+1)].

Originally Posted by Pikeman85

So I've been trying to differentiate this one problem, and then solve when the derivative is equal to 2. The equation in question is sqrt[(5x+1)/(4x^2+1)

Now for my answer before plugging in two I got .5((((20x^2+5)-(40x^2+8x))/(16x^4+8x^2+1))^(-1/2)

however this is obviously not a correct calculation - what was I doing wrong?

Differentiating we get



So remembering that

we see the answer is




so

Originally Posted by Pikeman85

So I've been trying to differentiate this one problem, and then solve when the derivative is equal to 2. The equation in question is sqrt[(5x+1)/(4x^2+1)

Now for my answer before plugging in two I got .5((((20x^2+5)-(40x^2+8x))/(16x^4+8x^2+1))^(-1/2)

however this is obviously not a correct calculation - what was I doing wrong?

Try taking it from here.

Originally Posted by Chris L T521

Try taking it from here.

Why do you put

instead of


I think the latter looks nicer...not that it matters...I am just curious

I punched you question into matlab, the derivative of your function

f(x) = sqrt(((5*x+1)/(4*x^2+1)))

is

f '(x) = 1/2/((5*x+1)/(4*x^2+1))^(1/2)*(5/(4*x^2+1)-8*(5*x+1)/(4*x^2+1)^2*x)

Im certain its 100% correct since a computer calculated it, if I'm wrong, let me know

Originally Posted by Mathstud28

Why do you put

instead of


I think the latter looks nicer...not that it matters...I am just curious

Its just a habbit. I do this a lot when I use mathtype, for it looks better that (').

Originally Posted by martinr

I punched you question into matlab, the derivative of your function

f(x) = sqrt(((5*x+1)/(4*x^2+1)))

is

f '(x) = 1/2/((5*x+1)/(4*x^2+1))^(1/2)*(5/(4*x^2+1)-8*(5*x+1)/(4*x^2+1)^2*x)

Im certain its 100% correct since a computer calculated it, if I'm wrong, let me know

Mathematica gave me this:



I assume its the same??

Hrm, here is another problem, this one is VERY difficult for me to solve.

[IMG]file:///D:/DOCUME%7E1/ANDREW%7E2.MAI/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG] Let F(x)= f(x^{5}) and G(x)=(f(x))^{5} . You also know that a^{4}=11, f(a)=3,f'(a)=10, f'(a^{5})=5.


Find F'(a)= and G'(a)=

Where do I even start with a problem like this one?

Originally Posted by Pikeman85

Hrm, here is another problem, this one is VERY difficult for me to solve.

[IMG]file:///D:/DOCUME%7E1/ANDREW%7E2.MAI/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG] Let F(x)= f(x^{5}) and G(x)=(f(x))^{5} . You also know that a^{4}=11, f(a)=3,f'(a)=10, f'(a^{5})=5.


Find F'(a)= and G'(a)=

Where do I even start with a problem like this one?

differentiating using the chain rule we get



so

and since they give us and

we have

I'd generally prefer it if people gave me more hints than answers. Oh work through part of a problem maybe, but eh. I want to figure this stuff out myself so that I actually KNOW it.

Now this one - this one is difficult for me (and thanks for everyone that has helped me this time and the time before! I'm actually getting some of the differentiation stuff quite a bit better now - still need to work on the Chain Rule, and a couple other things, but I have many of the others)

Ok so here's the problem I have now:

f(x) =
{ x^2 + 6x + 13 X (less than or equal to sign) 2
{ ax + b X (greater than) 2


Find a and b such that the function is differentiable everywhere. So I'm looking for continuity, and I know that at 2, the top equation = 28.

How do I go about solving this?

Originally Posted by Pikeman85

I'd generally prefer it if people gave me more hints than answers. Oh work through part of a problem maybe, but eh. I want to figure this stuff out myself so that I actually KNOW it.

Now this one - this one is difficult for me (and thanks for everyone that has helped me this time and the time before! I'm actually getting some of the differentiation stuff quite a bit better now - still need to work on the Chain Rule, and a couple other things, but I have many of the others)

Ok so here's the problem I have now:

f(x) =
{ x^2 + 6x + 13 X (less than or equal to sign) 2
{ ax + b X (greater than) 2


Find a and b such that the function is differentiable everywhere. So I'm looking for continuity, and I know that at 2, the top equation = 28.

How do I go about solving this?

You dont have to CAPITALIZE things ...I understand


Ok so you want a hint but not an answer

Here is your hint

if f(x) is differentiable at c then



and

Yes, I know that the two points have to touch, the problem is I am not sure how I am supposed to calculate which two points do touch

Originally Posted by Pikeman85

Yes, I know that the two points have to touch, the problem is I am not sure how I am supposed to calculate which two points do touch

Ok, so what you must do is this for it to be differentiable at the problem spot x=2

f(x) to the left of two must equal f(x) from the right of two

and f'(x) from the left of two must equal f'(x) from the right of two

so now you have to equations with two unknowns. Solve for the unknowns

Still not getting it. I'm very dense about a lot of the simpler bits. I've got most of the differentiation ones done, but this one eludes me