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

Problem

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

Solution

1. Identify the outer and inner functions to apply the chain rule. The expression is of the form un where u=sec(x) and n=4

2. Apply the power rule to the outer function by bringing the exponent to the front and decreasing the power by one.

4*sec(x)⋅d(sec(x))/d(x)

3. Apply the derivative rule for the trigonometric function sec(x) which is sec(x)*tan(x)

4*sec(x)⋅sec(x)*tan(x)

4. Simplify the expression by multiplying the powers of sec(x)

4*sec(x)*tan(x)

Final Answer

d(sec(x))/d(x)=4*sec(x)*tan(x)

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