Find the Derivative - d/dx 4sec(x)^2

Problem

d()/d(x)*4*sec2(x)

Solution

1. Identify the constant multiple rule and the power rule for the expression 4*(sec(x))2

2. Apply the power rule by bringing the exponent 2 to the front and multiplying it by the constant 4

4⋅2*sec(x)

3. Apply the chain rule by multiplying the result by the derivative of the inner function sec(x)

8*sec(x)⋅d(sec(x))/d(x)

4. Substitute the known derivative d(sec(x))/d(x)=sec(x)*tan(x)

8*sec(x)⋅sec(x)*tan(x)

5. Simplify the expression by combining the sec(x) terms.

8*sec2(x)*tan(x)

Final Answer

(d(4)*sec2(x))/d(x)=8*sec2(x)*tan(x)

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