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

Problem

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

Solution

1. Identify the outer and inner functions to apply the Power Rule and the Chain Rule. The expression is of the form un where u=sec(x) and n=3

2. Apply the Power Rule by bringing the exponent to the front and decreasing the power by one.

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

3. Differentiate the inner function sec(x) The derivative of sec(x) is sec(x)*tan(x)

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

4. Substitute the derivative of the inner function back into the expression.

3*sec(x)⋅sec(x)*tan(x)

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

3*sec(x)*tan(x)

Final Answer

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

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