Find the Derivative - d/dx sin(6x)

Problem

d(sin(6*x))/d(x)

Solution

1. Identify the outer function as sin(u) and the inner function as u=6*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 6*x with respect to x to get 6

5. Multiply the results together and substitute 6*x back in for u

Final Answer

d(sin(6*x))/d(x)=6*cos(6*x)

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