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

Problem

d(√(,sin(x)))/d(x)

Solution

1. Rewrite the square root as a fractional power to prepare for the chain rule.

√(,sin(x))=(sin(x))(1/2)

2. Apply the chain rule, which states that the derivative of ƒ*(g(x)) is ƒ′*(g(x))⋅g(x)′

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

3. Differentiate the inner function sin(x) with respect to x

d(sin(x))/d(x)=cos(x)

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

1/2*(sin(x))(−1/2)⋅cos(x)

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

cos(x)/(2√(,sin(x)))

Final Answer

d(√(,sin(x)))/d(x)=cos(x)/(2√(,sin(x)))

Want more problems? Check here!