Question

derivatives:
3. y= cot^3(2/x)
4. y= csc^5 (1-t+3t^2)
5. y=sec(5x)/tan3x

Answer 1

Use "function of a function" or "chain" differentiation rule.

Example

3. Let f(g) = g^3, where
g(h) = cos h
h(x) = 2/x
y = f{g(h(x))}
dy/dx = df/dg * dg/dh* dh/dx
= 3g^2*(-sin h)*(-2/x^2)
= 6*cos^2(2/x)*sin(2/x)/x^2