Find the 2nd Derivative y = square root of x+7

Problem

y=√(,x+7)

Solution

1. Rewrite the function using a fractional exponent to make differentiation easier.

y=(x+7)(1/2)

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

d(y)/d(x)=1/2*(x+7)(−1/2)⋅d(x+7)/d(x)

3. Simplify the first derivative, noting that the derivative of x+7 is 1

d(y)/d(x)=1/2*(x+7)(−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+7)(−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+7)(−3/2)

Final Answer

d2(y)/(d(x)2)=−1/(4*(x+7)(3/2))

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