Find the 2nd Derivative y = square root of x+2

Problem

d2()/(d(x)2)√(,x+2)

Solution

1. Rewrite the square root function as a power to make it easier to differentiate using the power rule.

y=(x+2)(1/2)

2. Apply the power rule and the chain rule to find the first derivative.

d(y)/d(x)=1/2*(x+2)(−1/2)⋅d(x+2)/d(x)

3. Simplify the first derivative, noting that the derivative of x+2 is 1

d(y)/d(x)=1/2*(x+2)(−1/2)

4. Differentiate again by applying the power rule to the first derivative to find the second derivative.

d2(y)/(d(x)2)=1/2⋅(−1/2)*(x+2)(−3/2)

5. Simplify the coefficients and rewrite the expression with a positive exponent in the denominator.

d2(y)/(d(x)2)=−1/4*(x+2)(−3/2)

Final Answer

d2()/(d(x)2)√(,x+2)=−1/(4*(x+2)(3/2))

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