# Thread: differentiation with trig functions

1. ## differentiation with trig functions

Hi, I finally sorted the following table out and filed in the values,

Now I have to find DT/DX (the rate of change of temperature) when X is equal to 150.

I've only really touched on differentiation, if anyone could talk me through this example you'd really be helpng me out.

Thanks.

2. Originally Posted by bobbymellor
Hi, I finally sorted the following table out and filed in the values,

Now I have to find DT/DX (the rate of change of temperature) when X is equal to 150.

I've only really touched on differentiation, if anyone could talk me through this example you'd really be helpng me out.

Thanks.
$10\sin{\frac{2\pi x}{365}} + 25$

You need to use the chain rule on $\frac{2\pi x}{365}$

$f'(x) = 10cos(\frac{2\pi x}{365}) \times \frac{2\pi}{365} = \frac{20\pi }{365} cos(\frac{2\pi x}{365})$

$f'(150) = \frac{20\pi }{365} cos(\frac{2\pi \times 150}{365})$

3. Hey, thanks for the quick reply. Is that an acceptable solution to this example, or will i need to continue to solve the last part, f'(150)= ......

4. Originally Posted by bobbymellor
Hey, thanks for the quick reply. Is that an acceptable solution to this example, or will i need to continue to solve the last part, f'(150)= ......
You'll need to solve f'(150), I don't have a calculator near me so I can't reduce it to terms of pi or a decimal approximation

5. ok thanks, would i be right in saying the rate of change for x = 150 is

62.83/365 cos (942.48/365)

or do I not need to change everything from its previous form?