15–48. Derivatives Find the derivative of the following functions.
s(t) = cos 2^t

Verified step by step guidance

1. Identify the function to differentiate: s(t) = cos(2^t).
2. Recognize that this is a composition of functions: the outer function is cos(u) and the inner function is u = 2^t.
3. Apply the chain rule, which states that if you have a composite function f(g(x)), the derivative is f'(g(x)) * g'(x).
4. Differentiate the outer function: the derivative of cos(u) is -sin(u).
5. Differentiate the inner function: the derivative of 2^t is 2^t * ln(2) using the exponential rule.