Question

Calculate d²y/dx² for y=3x−4ln(x).
a) 3-4/x²
b)−3+4/x²
c) 3+4/x²
d) −3−4/x²"

Answer 1

The second derivative of y=3x-4ln(x) is 4/x².

Step-by-step explanation:

To calculate d²y/dx² for y = 3x - 4ln(x), we need to find the second derivative of y with respect to x.

First, let's find the first derivative of y, which is dy/dx. The derivative of 3x is 3, and the derivative of -4ln(x) is -4/x.

Next, we find the second derivative by taking the derivative of the first derivative. The derivative of 3 is 0, and the derivative of -4/x is 4/x². Therefore, the second derivative of y is 0 + 4/x², which simplifies to 4/x².

Therefore, the correct answer is a) 3 - 4/x².