Given that p(x)=(3/((2x^2-5))), find p''(x)?

Use differentiation please....

1 Answer
Jun 8, 2018

p''(x) =(72x^2+60)/(2x^2-5)^3

Explanation:

Hi Loweena.

Here's one way to do this:
I would start by rewriting the equation without the division line:
p(x)=3*(2x^2-5)^-1

From that equation, and applying the chain rule, we can find the first derivative:
p'(x)=-3*(2x^2-5)^-2*4x
p'(x)=-12x*(2x^2-5)^-2

Now we repeat the process, applying the product rule and the chain rule, to get the second derivative:

p''(x) = -12*(2x^2-5)^-2 + (-12x)(-2)(2x^2-5)^-3*4x

p''(x) = -12*(2x^2-5)^-2 + 96x^2*(2x^2-5)^-3

If you wish, you can simplify this a little bit.
I will factor out (2x^2-5)^-3, and simplify what remains:

p''(x) = (2x^2-5)^-3*[-12*(2x^2-5)^1+96x^2]

p''(x) = (2x^2-5)^-3*[-24x^2+60+96x^2]

p''(x) =(2x^2-5)^-3*(72x^2+60)

If you wish, you can also return to the original format:

p''(x) =(72x^2+60)/(2x^2-5)^3