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

Problem

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

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, u=x2 and v=tan(x) use the product rule.

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

3. Differentiate the individual components. The derivative of x2 is 2*x using the power rule, and the derivative of tan(x) is sec2(x)

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

5. Simplify the resulting expression by arranging the terms.

Final Answer

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

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