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

Problem

d()/d(x)(x2)/cos(x)

Solution

1. Identify the rule needed for the derivative of a quotient of two functions, which is the quotient rule.

2. Apply the formula for the quotient rule, d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2) where u=x2 and v=cos(x)

3. Differentiate the numerator u=x2 to get d(u)/d(x)=2*x

4. Differentiate the denominator v=cos(x) to get d(v)/d(x)=−sin(x)

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

(cos(x)⋅2*x−x2⋅(−sin(x)))/((cos(x))2)

6. Simplify the expression by distributing the signs and rewriting the denominator.

(2*x*cos(x)+x2*sin(x))/cos2(x)

Final Answer

d()/d(x)(x2)/cos(x)=(2*x*cos(x)+x2*sin(x))/cos2(x)

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