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

Problem

d(√(,tan(x)))/d(x)

Solution

1. Rewrite the expression using a fractional exponent to make it easier to differentiate.

√(,tan(x))=(tan(x))(1/2)

2. Apply the chain rule by differentiating the outer function, which is the power of 1/2

d(tan(x))/d(x)=1/2*(tan(x))(−1/2)⋅d(tan(x))/d(x)

3. Differentiate the inner function, tan(x) which results in sec2(x)

1/2*(tan(x))(−1/2)⋅sec2(x)

4. Simplify the expression by moving the negative exponent to the denominator and rewriting it as a square root.

sec2(x)/(2√(,tan(x)))

Final Answer

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

Want more problems? Check here!