Find the Derivative - d/dx xcot(x)

Problem

d()/d(x)*x*cot(x)

Solution

1. Identify the rule needed for differentiation. Since the expression is a product of two functions, x and cot(x) we must use the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the functions for the product rule. Let u=x and v=cot(x)

3. Differentiate each part individually. The derivative of x is 1 and the derivative of cot(x) is −csc2(x)

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

xd(cot(x))/d(x)+cot(x)d(x)/d(x)

5. Substitute the derivatives into the expression.

x*(−csc2(x))+cot(x)*(1)

6. Simplify the resulting expression to find the final derivative.

−x*csc2(x)+cot(x)

Final Answer

(d(x)*cot(x))/d(x)=cot(x)−x*csc2(x)

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