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

Problem

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

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, 2*x and cos(x) the product rule (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x) must be applied.

2. Assign the variables for the product rule. Let u=2*x and v=cos(x)

3. Differentiate each part individually. The derivative of u is (d(2)*x)/d(x)=2 and the derivative of v is d(cos(x))/d(x)=−sin(x)

4. Apply the product rule formula by substituting the functions and their derivatives.

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

5. Simplify the resulting expression by rearranging the terms.

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

Final Answer

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

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