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

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 is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

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

4. Rewrite the inner function π/x as π*x(−1) to prepare for differentiation.

5. Differentiate the inner function using the power rule to get −π*x(−2) which is −π/(x2)

6. Combine the results of the chain rule.

Final Answer

d(sin(π/x))/d(x)=−(π*cos(π/x))/(x2)

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