2000ln(2t+3) derive it

Answer 1

To find the derivative of 2000ln(2t+3), we use the chain rule which states that if we have a function composed of two functions, we can differentiate it by applying the derivative of the outer function times the derivative of the inner function.

Let u = 2t + 3

Therefore, the function becomes 2000ln(u)

Now, differentiate the function with respect to t:

d/dt [2000ln(u)]
= 2000 * 1/u * du/dt
= 2000 * 1/(2t+3) * 2
= 4000 / (2t+3)

Therefore, the derivative of 2000ln(2t+3) with respect to t is 4000 / (2t+3).