Find the Derivative - d/dx square root of 1+x^2

Problem

d(√(,1+x2))/d(x)

Solution

1. Rewrite the square root as a power using the exponent 1/2

d(1+x2)/d(x)

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

1/2*(1+x2)(−1/2)⋅d(1+x2)/d(x)

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

1/2*(1+x2)(−1/2)⋅2*x

4. Simplify the expression by canceling the 1/2 and the 2

x*(1+x2)(−1/2)

5. Rewrite the negative exponent as a fraction to return to radical form.

x/√(,1+x2)

Final Answer

d(√(,1+x2))/d(x)=x/√(,1+x2)

Want more problems? Check here!