Find the Derivative - d/dx sin(pix)

Problem

d(sin(π*x))/d(x)

Solution

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

5. Multiply the results together and substitute u=π*x back into the expression.

Final Answer

d(sin(π*x))/d(x)=π*cos(π*x)

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