Question

Find the derivative of the function h(t)= 4/t + 9/t^2

Answer 1

The derivative of the function h(t) = 4/t + 9/t^2 is h'(t) = -4/t^2 - 18/t^3.

Step-by-step explanation:

To find the derivative of the function h(t) = 4/t + 9/t^2 with respect to t, we apply the basic rules of differentiation. Each term of the function is a power of t, so we can use the power rule for derivatives. For the first term, 4/t is the same as 4t^-1, and for the second term, 9/t^2 is the same as 9t^-2.

Using the power rule, which states that d/dx (x^n) = nx^(n-1), we get:

• The derivative of 4t^-1 is -4t^-2, which is -4/t^2.
• The derivative of 9t^-2 is -18t^-3, which is -18/t^3.

Therefore, the derivative of h(t) is:

h'(t) = -4/t^2 - 18/t^3