Derivative with chain rule: sin(ln(x)). Trigonometric function and natural log chain rule problem.

We compute the derivative of sin(ln(x)) by using the chain rule. First we differentiate with respect to the argument of sin(ln(x)), treating the natural log function as a single variable (ln(x) is the chain rule inner function here). Then, we tack on the derivative of that argument with respect to x, giving us an extra factor of 1/x. We clean things up a bit, and we're done!