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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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$\frac{\frac{d}{dt}\left(-te^t\right)\left(2t^2e^t+4te^t\right)-\left(-1\right)te^t\frac{d}{dt}\left(2t^2e^t+4te^t\right)}{\left(2t^2e^t+4te^t\right)^2}$
Learn how to solve problems step by step online. Find the derivative using the product rule d/dt((-te^t)/(2t^2e^t+4te^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}}. Multiply -1 times -1. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The derivative of the constant function (-1) is equal to zero.