Solving the Derivative of f(a): A Frustrating Homework Problem

[fghtffyrdmns]

Homework Statement

For some reason, I cannot seem to get the derivative for this.

Homework Equations

f(a) =\frac {(2500+0.2t)(1+t)}{\sqrt {0.5t+2}}

The Attempt at a Solution

f(a) =\frac {(2500+0.2t)(1+t)}{\sqrt {0.5t+2}}

\frac {(2500+0.2t)}{\sqrt {0.5t+2}} (1+t)

From here I would just use the quotient rule but I keep getting the wrong answer and I have no idea why.

 

[RPierre]

I'll simplify this for you. See if you can solve the question from here:

First, FOIL the numerator. Next, solve all of our components separately, so:

h'(x) = \frac{d}{dx} (0.5t + 2)^1/2

= \frac{1}{2}(0.5t +2)^-1/2 * 0.5 <By Chain Rule>

= \frac{1}{4} \frac{1}{\sqrt{(0.5t+2)}} <By x^-1 = 1/x>

g'(x) = 0.4t + 2500.2 <By power rule x^2 = 2x when the derivative is taken>

h(x)² = 0.5t + 2 <x^1/2^2 = x^1>

next, plug in all of that data to the quotient rule, simplify, and see what you get!

 

[fghtffyrdmns]

ahhh, thank you!

at first, I thought I was supposed to treat it separately. Now, I just expanded the numerator and took the derivatives of both sides.

Thank you, sir :).

 

[Mark44]

Both of you should get your variables straight.

f(a) =\frac {(2500+0.2t)(1+t)}{\sqrt {0.5t+2}}

That would be f(t), not f(a).

h'(x) = \frac{d}{dx}(0.5t + 2)^1/2

And that would be h&#039;(t) = \frac{d}{dt}(0.5t + 2)^{1/2}

 

[RPierre]

I'm not familiar with LaTex and assumed he wasn't using leibniz notation by the prime notation used and the level of calculus, so I simply whipped up a solution with simple principles. I'm sure the original poster got the point as the question was able to be resolved.

Thanks for pointing that out though, I'll be more precise with my answers in the future, I'm also new to these forums.

 

[fghtffyrdmns]

ah yes, it's my fault. I wrote the wrong variables in accidentally.I got this as my answer

\frac {(0.5t+2)^{1/2}(0.4t+2500.2)-(2500+2500.2t+0.2t^{2})}{(2t+8)^{3/2}}

 

[fghtffyrdmns]

Hmm. This is not the right derivative. Where did I go wrong?