Final answer:
The derivative of the function f(x) = sin(7 ln(x)) is found using the chain rule and is f'(x) = cos(7 ln(x)) × (7/x).
Step-by-step explanation:
To differentiate the function f(x) = sin(7 ln(x)), we need to use the chain rule. The chain rule in calculus is a formula for computing the derivative of the composition of two or more functions. Let u = 7 ln(x), which makes f(x) = sin(u).
The derivative of f(x) with respect to x is found by multiplying the derivative of sin(u) with respect to u by the derivative of u with respect to x. Since the derivative of sin(u) is cos(u) and the derivative of 7 ln(x) with respect to x is 7/x, the derivative of f(x) is f'(x) = cos(7 ln(x)) × (7/x).