Find the Derivative - d/dx sec(x)

Problem

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

Solution

1. Rewrite the secant function in terms of the cosine function using the reciprocal identity.

sec(x)=1/cos(x)

2. Apply the power rule and the chain rule by treating the expression as (cos(x))(−1)

d(cos(x))/d(x)=−1*(cos(x))(−2)⋅d(cos(x))/d(x)

3. Differentiate the inner function cos(x) which results in −sin(x)

−(cos(x))(−2)⋅(−sin(x))

4. Simplify the expression by combining the negative signs and rewriting the exponents.

sin(x)/cos2(x)

5. Separate the fraction into a product of two trigonometric ratios to reach the standard form.

1/cos(x)⋅sin(x)/cos(x)

6. Substitute the identities sec(x)=1/cos(x) and tan(x)=sin(x)/cos(x)

sec(x)*tan(x)

Final Answer

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

Want more problems? Check here!