Question

Find yʹ'' if y=x⁻⁸+x⁸

Answer 1

The second derivative of the function y = x^{-8} + x^{8} is y'' = 72x^{-10} + 56x^{6}.

Step-by-step explanation:

To find the second derivative of the function y = x^{-8} + x^{8}, we need to differentiate y twice with respect to x. Let's proceed with the differentiation step by step:

First Derivative (y')

The first derivative of y with respect to x is:

• d/dx(x^{-8}) = -8x^{-9}
• d/dx(x^{8}) = 8x^{7}

So, the first derivative y' is:

y' = -8x^{-9} + 8x^{7}

Second Derivative (y'')

Now we differentiate y' to find the second derivative y'':

• d/dx(-8x^{-9}) = 72x^{-10}
• d/dx(8x^{7}) = 56x^{6}

Thus, the second derivative y'' is:

y'' = 72x^{-10} + 56x^{6}