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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$

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$\frac{\frac{d}{dt}\left(\sqrt{t-4}\right)t\cos\left(t\right)-\sqrt{t-4}\frac{d}{dt}\left(t\cos\left(t\right)\right)}{\left(t\cos\left(t\right)\right)^2}$

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=. Simplify the product -(\frac{d}{dt}\left(t\right)\cos\left(t\right)+t\frac{d}{dt}\left(\cos\left(t\right)\right)).

** Final answer to the problem

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