Find the derivative of y = cos(ax - b) from the first princip?​

Recall that

sin(x ± y) = sin(x) cos(y) ± cos(x) sin(y)

cos(x ± y) = cos(x) cos(y) ∓ sin(x) sin(y)

Then

cos(ax - b) = cos(ax) cos(b) + sin(ax) sin(b)

When you differentiate y with respect to x, you only need to focus on the the cos(ax) and sin(ax) terms.

We have

Now, recall these useful known limits: for c ≠ 0,

Then the limits involving cosine vanish, and the derivative simplifies to

For the remaining limits, introduce a factor of a in the denominators:

and using the first identity listed above, we can write this as

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175