Question

Differentiate. f(t) = 3 √t/ (t - 6)

Answer 1

To differentiate the function f(t) = 3√t / (t - 6), use the quotient rule. The derivative of f(t) is (3(t - 6) - 2√t(t - 6)) / (t - 6)^2.

Step-by-step explanation:

To differentiate the function f(t) = 3√t / (t - 6), we can use the quotient rule. Let's first denote u(t) = 3√t and v(t) = (t - 6). The derivative of f(t) is given by the formula (u'(t)v(t) - u(t)v'(t)) / (v(t))^2.

Using the power rule, we can find u'(t) = (1/2) * 3 * t^(-1/2) = 3 / (2√t). The derivative of v(t) is simply 1.

Plugging these values into the quotient rule, we get (3 / (2√t) * (t - 6) - (3√t) * 1) / (t - 6)^2.

Simplifying further, the derivative of f(t) is (3(t - 6) - 2√t(t - 6)) / (t - 6)^2.