1) Find the first and second derivatives:

y = Square Root((x^2) + 1)

2) If f(x) = Square Root(1 + (x^3)) , find the second derivative (2). So x = 2.

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- Mar 4th 2009, 11:01 AMDicksonHigher Derivatives
1) Find the first and second derivatives:

y = Square Root((x^2) + 1)

2) If f(x) = Square Root(1 + (x^3)) , find the second derivative (2). So x = 2. - Mar 4th 2009, 11:14 AMHallsofIvy
$\displaystyle y= (x^2+ 1)^{1/2}$

Apply the power rule, $\displaystyle (u^n)'= nu^{n-1}$ and the chain rule. - Mar 4th 2009, 02:56 PMDickson
Did that and got the wrong answer

- Mar 4th 2009, 05:09 PMHallsofIvy
Then show what you did, please.

- Mar 4th 2009, 06:40 PMDickson
First Deriv. = (1/2)(x^2 + 1) ^ (-1/2) (2x)

= x(x^2 + 1) ^ (-1/2)

Second = (-1/2x) (x^2 + 1) ^ (-3/2) (2x)

= -x^2 (x^2 + 1) ^ (-3/2)

Book says it should be only an x in the front - Mar 5th 2009, 02:25 AMmr fantastic
To get the second derivative you have to use either the product or quotient rule as well as the chain rule.

I suggest writing the first derivative as $\displaystyle \frac{x}{(x^2 + 1)^{1/2}}$ and using the quotient rule to differentiate. To get the derivative of the denominator the chain rule is required.

A bit of algebra will be required to get the answer in the required form.