Find the Derivative - d/dx sec( square root of x)

Problem

d(sec(√(,x)))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is sec(u) and the inner function is u=√(,x)

2. Apply the Chain Rule which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

3. Differentiate the outer function sec(u) with respect to u which results in sec(u)*tan(u)

4. Differentiate the inner function √(,x) which is x(1/2) using the Power Rule to get 1/2*x(−1/2) or 1/(2√(,x))

5. Substitute the inner function back into the derivative of the outer function and multiply the components together.

6. Simplify the expression into a single fraction.

Final Answer

d(sec(√(,x)))/d(x)=(sec(√(,x))*tan(√(,x)))/(2√(,x))

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