Find the Derivative - d/dx y=sec(x)

Problem

d(sec(x))/d(x)

Solution

1. Identify the function to be differentiated, which is the trigonometric function y=sec(x)

2. Apply the definition of the secant function in terms of the cosine function, where sec(x)=1/cos(x)

3. Use the quotient rule or the power rule with the chain rule to differentiate (cos(x))(−1)

4. Differentiate the expression to get −1*(cos(x))(−2)⋅(−sin(x))

5. Simplify the resulting expression by rearranging the terms into sin(x)/cos2(x)

6. Rewrite the expression using trigonometric identities to obtain 1/cos(x)⋅sin(x)/cos(x)

7. Substitute the identities sec(x) and tan(x) to reach the final derivative form.

Final Answer

d(sec(x))/d(x)=sec(x)*tan(x)

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