Find the Derivative - d/dt sec(t)^2

Problem

d(sec(t))/d(t)

Solution

1. Identify the outer and inner functions to apply the chain rule, where the outer function is u2 and the inner function is u=sec(t)

2. Apply the power rule to the outer function, which gives 2*sec(t) multiplied by the derivative of the inner function.

3. Differentiate the inner function sec(t) using the trigonometric derivative rule d(sec(t))/d(t)=sec(t)*tan(t)

4. Multiply the results together to get 2*sec(t)⋅sec(t)*tan(t)

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

Final Answer

d(sec(t))/d(t)=2*sec(t)*tan(t)

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