Question

Calculate d²y/dx² for y= x³−4ln(x).

a) 6x²− 1/x³
b) −6x²+1/x³
c) 6x² +1/x³
d) −6x²−1/x³

Answer 1

The second derivative of the function y = x³ - 4ln(x) is obtained by first finding the first derivative and then differentiating it again, resulting in the answer c) 6x² + 1/x³.

Step-by-step explanation:

To calculate the second derivative of the function y = x³ - 4ln(x), we first find the first derivative and then differentiate it once more.

The first derivative (αy/αx) is:

• 3x² - (4/x)

Now, we find the second derivative (β²y/αx²):

• 6x - (-4/x²)
• 6x² + 4/x³

So, the correct answer is c) 6x² + 1/x³.