Find the Derivative - d/dx x-2cos(x)

Problem

d()/d(x)*(x−2*cos(x))

Solution

1. Apply the sum rule for differentiation, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(x−2*cos(x))=d(x)/d(x)−(d(2)*cos(x))/d(x)

2. Differentiate the first term using the power rule, where the derivative of x with respect to x is 1.

d(x)/d(x)=1

3. Apply the constant multiple rule to the second term, moving the constant 2 outside the derivative.

(d(2)*cos(x))/d(x)=2d(cos(x))/d(x)

4. Differentiate the trigonometric function using the rule that the derivative of cos(x) is −sin(x)

2d(cos(x))/d(x)=2*(−sin(x))

5. Simplify the expression by combining the results and applying the double negative.

1−(−2*sin(x))=1+2*sin(x)

Final Answer

d()/d(x)*(x−2*cos(x))=1+2*sin(x)

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