Learn how to solve problems step by step online. Find the derivative d/dt(((t-4)^(1/2))/(tcos(t))). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The power of a product is equal to the product of it's factors raised to the same power. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=t and g=\cos\left(t\right). Simplify the product -(\frac{d}{dt}\left(t\right)\cos\left(t\right)+t\frac{d}{dt}\left(\cos\left(t\right)\right)).

Find the derivative d/dt(((t-4)^(1/2))/(tcos(t)))