Derivative of a Function with Chain Rule

Find the derivative of $s(6x)$.

Finding the derivative of a composed function, like $s(6x)$, involves applying the chain rule, which is a fundamental tool in calculus. The chain rule allows us to differentiate composite functions by relating the derivative of the outer function to the derivative of the inner function. In this case, you have an inside function, 6x, and an outer function, s. The solution would involve multiplying the derivative of the outer function, s, evaluated at the inside function, 6x, by the derivative of the inside function, 6x. This method is incredibly useful when dealing with functions where one is nested within another and helps simplify the differentiation process.

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