Find the Derivative - d/dy y=(sin(x))/2+c/x

Problem

d()/d(x)*(sin(x)/2+c/x)

Solution

1. Identify the expression as a sum of two terms and apply the sum rule for derivatives.

2. Apply the constant multiple rule to the first term, sin(x)/2 noting that 1/2 is a constant.

3. Differentiate sin(x) to get cos(x)

4. Rewrite the second term, c/x as c*x(−1) to prepare for the power rule.

5. Apply the power rule to c*x(−1) which results in −1⋅c*x(−2)

6. Simplify the expression by rewriting the negative exponent as a fraction.

Final Answer

d()/d(x)*(sin(x)/2+c/x)=cos(x)/2−c/(x2)

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