If I had to simplify 15/24 it would be 5/8
It's hard to type and hard to read the "inverse tangent" function, as you've seen (above).
So, use "arctan x" instead.
Then the problem becomes: "differentiate cos (arctan x)."
You must apply first the rule for differentiating the cosine function, and next apply the rule for differentiating the arctan function:
(d/dx) cos (arctan x) = - sin (arctan x) * [1/(1+x^2)]
I believe it is 960 inches. For the long triangles, I just made them a square so I multiplied base times height. For the small triangles, i did the same thing. Long triangles were 640, small triangles were 320

Differentiate both sides with respect to <em>x</em>, assuming <em>y</em> = <em>y</em>(<em>x</em>).




Solve for d<em>y</em>/d<em>x</em> :



If <em>y</em> ≠ 0, we can write

At the point (1, 1), the derivative is

Given:
x and y are both differentiable functions of t.


To find:
The value of
.
Solution:
We have,
...(i)
At x=-1,




Divide both sides by 3.

Taking cube root on both sides.

So, y=2 at x=-1.
Differentiate (i) with respect to t.

Putting x=-1, y=2 and
, we get



Divide both sides by -8.


Therefore, the value of
is 36.