Find the Derivative - d/dx y=sin(9x)

Problem

d(sin(9*x))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sin(u) and the inner function is u=9*x

2. Apply the Chain Rule, which states that the derivative of sin(u) is cos(u)⋅d(u)/d(x)

3. Differentiate the outer function with respect to the inner function, resulting in cos(9*x)

4. Differentiate the inner function 9*x with respect to x which results in 9

5. Multiply the results of the derivatives together to find the final derivative.

Final Answer

d(sin(9*x))/d(x)=9*cos(9*x)

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