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

Problem

(d(x2)*tan(x))/d(x)

Solution

1. Identify the rule needed for the expression, which is the product of two functions: u=x2 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 by finding d(x2)/d(x)=2*x using the power rule.

4. Differentiate the second part by finding d(tan(x))/d(x)=sec2(x) using trigonometric derivative rules.

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

6. Simplify the resulting expression by combining the terms.

Final Answer

(d(x2)*tan(x))/d(x)=x2*sec2(x)+2*x*tan(x)

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