# discussion question. The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. A. sin(x²) is a composite function becaus

discussion question.

The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*.

A.  sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x². Using the chain rule and the derivatives of sin(x) and x², find its derivative.B.  cos (sin(x2))  requires the chain rule twice because x2  is inside sin and sin x2 is inside cos.   Find this derivative.C.  cos x sin x    does  not need the chain rule, just the product rule.   Find this derivative.D.  cos x sin x2   requires both the product rule and the chain rule.  Find this derivative.

Identify which derivative below goes with A, B, C, and D:

1) -sin x sin x + cos x cos x2) 2x (cos(x²))3) -sin (sin(x2)) (cos(x²)) (2x)4) -sin x sin(x2)+ cos x (2x cos(x2))