1. ## differentiating this equation

HI I have attached a picture of the equation which I have problem with.

I need to differentiate T with respect to T0, so dT/dT0

D, L, lambda and C are constants.

I would apperciate if anyone can help me differentiating the above equation

(link to the image Yfrog Image : yfrog.com/mvequationj)

2. We differentiate the LHS with the chain rule:

$\displaystyle \frac{d}{dT_0}T^2 = 2 T \frac{dT}{dT_0}$

We differentiate the RHS with the usual power rule:

$\displaystyle \displaystyle \frac{d}{dT_0}( T_0^2+f T_0^{-2} ) = 2 T_0 - 2 f T_0^{-3}$

f is just the combined constants. Equating both sides and canceling the 2, we get

$\displaystyle \displaystyle T \frac{dT}{dT_0} = T_0 - f T_0^{-3}$

We still have a free $\displaystyle T$, so we need to replace it with an expression derived from the first equation.

$\displaystyle \displaystyle \frac{dT}{dT_0} = T^{-1} (T_0 - f T_0^{-3}) = ( T_0^2+f T_0^{-2})^{-1/2}(T_0 - f T_0^{-3})$

And I think you are done.

3. Thans