Find the Derivative - d/dx y=sin( natural log of x)

Problem

d()/d(x)*sin(ln(x))

Solution

1. Identify the outer function as sin(u) and the inner function as u=ln(x)

2. Apply the chain rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function sin(u) with respect to u to get cos(u)

4. Differentiate the inner function ln(x) with respect to x to get 1/x

5. Multiply the results together and substitute u=ln(x) back into the expression.

Final Answer

d(sin(ln(x)))/d(x)=cos(ln(x))/x

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