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

Problem

d(tan(√(,x)))/d(x)

Solution

1. Identify the outer function as tan(u) and the inner function as u=√(,x) which can be written as x(1/2)

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 tan(u) with respect to u to get sec2(u)

4. Differentiate the inner function x(1/2) using the power rule to get 1/2*x(−1/2) which simplifies to 1/(2√(,x))

5. Multiply the results of the derivatives together and substitute u=√(,x) back into the expression.

6. Simplify the final expression by combining the terms into a single fraction.

Final Answer

d(tan(√(,x)))/d(x)=sec2(√(,x))/(2√(,x))

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