1. differentiation in trigonomerty help???

T = 10Sin ( (2Pi/365)*X ) + 25 , is the daily average temperature in a village where X is the day of the year.

I have constructed a table of values for 0 < X < 365 and created a graph, however when it comes to differentiating the following I am a bit lost. If someone could talk me through it that would be great:

i) The rate of change of the temperature is given by dT/dX . Find dT/dX and the rate of change of the temperature when X = 150 .

2. Originally Posted by bobbymellor
T = 10Sin ( (2Pi/365)*X ) + 25 , is the daily average temperature in a village where X is the day of the year.

I have constructed a table of values for 0 < X < 365 and created a graph, however when it comes to differentiating the following I am a bit lost. If someone could talk me through it that would be great:

i) The rate of change of the temperature is given by dT/dX . Find dT/dX and the rate of change of the temperature when X = 150 .
By chain rule, $\displaystyle T=10\sin\left(\frac{2\pi}{365}X\right)+25\implies \frac{\,dT}{\,dX}=10\cos\left(\frac{2\pi}{365}X\ri ght)\cdot\frac{\,d}{\,dX}\left[\frac{2\pi}{365}X\right]$

Can you continue and find $\displaystyle T^{\prime}\!\left(150\right)$??

3. Hi again, coming back to this problem, honestly I'm still a bit lost when it comes to differentiating anything but the very basic examples, Im very comfortable with anything trig' based but still having problems with differentiation.