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)].
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)].
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
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?
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?
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