Find the Derivative - d/dx square root of x^2+8

Problem

d(√(,x2+8))/d(x)

Solution

1. Rewrite the square root as a power using the rule √(,u)=u(1/2)

d(x2+8)/d(x)

2. Apply the chain rule, which states that d(un)/d(x)=n*u(n−1)⋅d(u)/d(x)

1/2*(x2+8)(−1/2)⋅d(x2+8)/d(x)

3. Differentiate the inner function x2+8 with respect to x

1/2*(x2+8)(−1/2)⋅2*x

4. Simplify the expression by multiplying the constants and moving the negative exponent to the denominator.

(2*x)/(2*(x2+8)(1/2))

5. Cancel the common factor of 2 and convert the fractional power back into a square root.

x/√(,x2+8)

Final Answer

d(√(,x2+8))/d(x)=x/√(,x2+8)

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