Find the Derivative - d/dx y=1-sin(x)

Problem

d()/d(x)*(1−sin(x))

Solution

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

d()/d(x)*(1−sin(x))=d(1)/d(x)−d(sin(x))/d(x)

2. Differentiate the constant term, noting that the derivative of any constant is zero.

d(1)/d(x)=0

3. Differentiate the trigonometric term using the standard derivative rule for the sine function.

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

4. Combine the results to find the final derivative.

0−cos(x)=−cos(x)

Final Answer

d()/d(x)*(1−sin(x))=−cos(x)

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