Find the Derivative - d/dx x^2sin(2x)

Problem

d()/d(x)*x2*sin(2*x)

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, x2 and sin(2*x) use the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Differentiate the first part of the product.

d(x2)/d(x)=2*x

3. Differentiate the second part of the product using the chain rule.

d(sin(2*x))/d(x)=cos(2*x)⋅2

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

4. Apply the product rule formula by combining the parts.

(d(x2)*sin(2*x))/d(x)=x2*(2*cos(2*x))+sin(2*x)*(2*x)

5. Simplify the expression by rearranging the terms.

(d(x2)*sin(2*x))/d(x)=2*x2*cos(2*x)+2*x*sin(2*x)

Final Answer

(d(x2)*sin(2*x))/d(x)=2*x2*cos(2*x)+2*x*sin(2*x)

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