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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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$\frac{\frac{d}{dx}\left(e^x\right)\left(3-e^x\right)-e^x\frac{d}{dx}\left(3-e^x\right)}{\left(3-e^x\right)^2}$
Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx((e^x)/(3-e^x)). 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}}. Applying the derivative of the exponential function. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Simplify the product -(\frac{d}{dx}\left(3\right)+\frac{d}{dx}\left(-e^x\right)).