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

Problem

d()/d(x)*x^2*tan(x)

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, u=x^2 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 x^2 is 2*x using the power rule, and the derivative of tan(x) is sec^2(x)

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

5. Simplify the resulting expression by arranging the terms.

Final Answer

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

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