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

Problem

d()/d(x)*x^3*tan(x)

Solution

1. Identify the rule needed for the expression, which is the product of two functions: u=x^3 and v=tan(x)

2. Apply the product rule, which states that (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the first part of the product: d(x^3)/d(x)=3*x^2

4. Differentiate the second part of the product: d(tan(x))/d(x)=sec^2(x)

5. Substitute these derivatives back into the product rule formula: x^3*sec^2(x)+tan(x)*(3*x^2)

6. Simplify the expression by rearranging the terms.

Final Answer

(d(x^3)*tan(x))/d(x)=x^3*sec^2(x)+3*x^2*tan(x)

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