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

Problem

d(cos(√(,x)))/d(x)

Solution

1. Identify the outer function as cos(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 cos(u) with respect to u to get −sin(u)

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

5. Combine the results and substitute u=√(,x) back into the expression.

6. Simplify the expression by moving the negative exponent to the denominator.

Final Answer

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

Want more problems? Check here!