Find the Derivative - d/dx y=7sec(x)

Problem

d()/d(x)*7*sec(x)

Solution

1. Identify the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of that function.

2. Apply the constant multiple rule by moving the 7 outside of the derivative operation.

(d(7)*sec(x))/d(x)=7d(sec(x))/d(x)

3. Recall the trigonometric derivative rule for the secant function, which is d(sec(x))/d(x)=sec(x)*tan(x)

4. Substitute the derivative of sec(x) back into the expression.

7d(sec(x))/d(x)=7*sec(x)*tan(x)

Final Answer

(d(7)*sec(x))/d(x)=7*sec(x)*tan(x)

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