A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The
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The derivative is given by the limit
You have
Use the angle sum identity for tangent. I don't remember it off the top of my head, but I do remember the ones for (co)sine.
By this identity, you have
So in the limit you get
The first two limits are both 1, and the single term in the last limit approaches 0 as
which agrees with the result you get from applying the chain rule.