see explanation
Step-by-step explanation:
Using the chain rule and the standard derivatives
Given
y = f(g(x)) , then
= f'(g(x)) × g'(x) ← chain rule
(tanx) = sec²x , (cotx) = - csc²x
(c)
y = tan = tan
= sec² × ( )
= sec² ×
= sec² ×
=
(d)
y = cot(1 + x)
= - csc²(1 + x) × (1 + x)
= - csc²(1 + x) × 1
= - csc²(1 + x)