Find the Derivative - d/dx square root of x^2+9

Problem

d(√(,x2+9))/d(x)

Solution

1. Rewrite the expression using a fractional exponent to make it easier to differentiate.

√(,x2+9)=(x2+9)(1/2)

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

d(x2+9)/d(x)=1/2*(x2+9)(−1/2)⋅d(x2+9)/d(x)

3. Differentiate the inner function x2+9 with respect to x

d(x2+9)/d(x)=2*x

4. Substitute the derivative of the inner function back into the expression.

1/2*(x2+9)(−1/2)⋅2*x

5. Simplify the expression by canceling the constant factors and moving the negative exponent to the denominator.

x/((x2+9)(1/2))

6. Convert the fractional exponent back into radical notation.

x/√(,x2+9)

Final Answer

d(√(,x2+9))/d(x)=x/√(,x2+9)

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