Find the 2nd Derivative y = square root of x+6

Problem

d2()/(d(x)2)√(,x+6)

Solution

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

y=(x+6)(1/2)

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

d(y)/d(x)=1/2*(x+6)(−1/2)

3. Apply the power rule again to the first derivative to find the second derivative.

d2(y)/(d(x)2)=1/2⋅(−1/2)*(x+6)(−3/2)

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

d2(y)/(d(x)2)=−1/(4*(x+6)(3/2))

Final Answer

d2()/(d(x)2)√(,x+6)=−1/(4*(x+6)(3/2))

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