Find the Derivative - d/dx 1-cos(x)

Problem

d()/d(x)*(1−cos(x))

Solution

1. Apply the sum/difference rule for derivatives, which allows us to differentiate each term of the expression separately.

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

2. Differentiate the constant term. The derivative of any constant with respect to x is 0

d(1)/d(x)=0

3. Differentiate the trigonometric function cos(x) The derivative of cos(x) with respect to x is −sin(x)

d(cos(x))/d(x)=−sin(x)

4. Combine the results and simplify the signs.

0−(−sin(x))=sin(x)

Final Answer

d()/d(x)*(1−cos(x))=sin(x)

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