Find the Derivative - d/dx square root of 3x+2cos(x)

Problem

d(√(,3*x+2*cos(x)))/d(x)

Solution

1. Identify the outer and inner functions to apply the Chain Rule. The outer function is the square root, u(1/2) and the inner function is u=3*x+2*cos(x)

2. Differentiate the outer function with respect to the inner function. The derivative of √(,u) is 1/(2√(,u))

3. Differentiate the inner function 3*x+2*cos(x) with respect to x The derivative is 3−2*sin(x)

4. Multiply the derivative of the outer function by the derivative of the inner function according to the Chain Rule.

d(√(,3*x+2*cos(x)))/d(x)=1/(2√(,3*x+2*cos(x)))⋅(3−2*sin(x))

5. Simplify the expression into a single fraction.

Final Answer

d(√(,3*x+2*cos(x)))/d(x)=(3−2*sin(x))/(2√(,3*x+2*cos(x)))

Want more problems? Check here!