Find the Derivative - d/dx sin(7 natural log of x)

Problem

d(sin(7*ln(x)))/d(x)

Solution

1. Identify the outer function as sin(u) and the inner function as u=7*ln(x)

2. Apply the chain rule, which states that (d(ƒ)*(g(x)))/d(x)=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 7*ln(x) with respect to x to get 7/x

5. Multiply the results together and substitute u=7*ln(x) back into the expression.

Final Answer

d(sin(7*ln(x)))/d(x)=(7*cos(7*ln(x)))/x

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