Find the derivative of the given function with respect to the independent variable x or t. the symbols a, b and c are constants greater than 1. you are not required to combine like terms, reduce fractions, or otherwise simplify your final answer.
(1) y = (2/[ a+bx])^3
(2) y = (at^3 - 3bt)^3
(3) y = (t^b)e^(b/t)
(4) z = ax^2.sin (4x)

(1)

By differentiating w.r.t. x,

(2)

By differentiating w.r.t. t,

(3)

Differentiating w.r.t. t,

(4)

Differentiating w.r.t. x,

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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