Find the Derivative - d/dx f(x) = square root of x^2+1

Problem

d(√(,x2+1))/d(x)

Solution

1. Identify the function as a composition of functions where the outer function is the square root, u(1/2) and the inner function is u=x2+1

2. Apply the power rule and the chain rule, which states that d(√(,u))/d(x)=1/(2√(,u))⋅d(u)/d(x)

3. Differentiate the inner function x2+1 with respect to x to get 2*x

4. Substitute the inner function and its derivative back into the chain rule formula: 1/(2√(,x2+1))⋅2*x

5. Simplify the expression by canceling the factor of 2 in the numerator and denominator.

Final Answer

d(√(,x2+1))/d(x)=x/√(,x2+1)

Want more problems? Check here!