Find the Derivative - d/dx sec(3x)

Problem

d(sec(3*x))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sec(u) and the inner function is u=3*x

2. Apply the derivative rule for the secant function, which states d(sec(u))/d(u)=sec(u)*tan(u)

3. Apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function.

d(sec(3*x))/d(x)=sec(3*x)*tan(3*x)⋅(d(3)*x)/d(x)

4. Differentiate the inner function 3*x with respect to x which results in 3

d(sec(3*x))/d(x)=sec(3*x)*tan(3*x)⋅3

5. Simplify the expression by moving the constant to the front.

d(sec(3*x))/d(x)=3*sec(3*x)*tan(3*x)

Final Answer

d(sec(3*x))/d(x)=3*sec(3*x)*tan(3*x)

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