Find the Derivative - d/dx x^3cos(x)

Problem

d()/d(x)*x3*cos(x)

Solution

1. Identify the rule needed for the expression, which is the product of two functions: ƒ(x)=x3 and g(x)=cos(x)

2. Apply the product rule, which states that d()/d(x)*ƒ(x)*g(x)=ƒ(x)d(g(x))/d(x)+g(x)d(ƒ(x))/d(x)

3. Differentiate the individual components: d(x3)/d(x)=3*x2 and d(cos(x))/d(x)=−sin(x)

4. Substitute these derivatives back into the product rule formula.

5. Simplify the resulting expression by rearranging the terms.

Final Answer

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

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