Find the Derivative - d/dx 2x^3sin(x)-3xcos(x)

Problem

d()/d(x)*(2*x3*sin(x)−3*x*cos(x))

Solution

1. Apply the sum rule to differentiate the two terms separately.

d()/d(x)*(2*x3*sin(x)−3*x*cos(x))=(d(2)*x3*sin(x))/d(x)−(d(3)*x*cos(x))/d(x)

2. Apply the product rule to the first term, where (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

(d(2)*x3*sin(x))/d(x)=2*x3*cos(x)+6*x2*sin(x)

3. Apply the product rule to the second term.

(d(3)*x*cos(x))/d(x)=3*x*(−sin(x))+3*cos(x)

4. Combine the results and distribute the negative sign.

2*x3*cos(x)+6*x2*sin(x)−(−3*x*sin(x)+3*cos(x))

5. Simplify the expression by combining like terms and signs.

2*x3*cos(x)+6*x2*sin(x)+3*x*sin(x)−3*cos(x)

Final Answer

d()/d(x)*(2*x3*sin(x)−3*x*cos(x))=2*x3*cos(x)+6*x2*sin(x)+3*x*sin(x)−3*cos(x)

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