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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 ${\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}$
Applying the derivative of the exponential function
Learn how to solve quotient rule of differentiation problems step by step online.
$\frac{\frac{d}{dx}\left(e^{\left(x+y\right)}\right)\left(2y-e^{\left(x+y\right)}\right)-e^{\left(x+y\right)}\frac{d}{dx}\left(2y-e^{\left(x+y\right)}\right)}{\left(2y-e^{\left(x+y\right)}\right)^2}$
Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx((e^(x+y))/(2y-e^(x+y))). 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. The derivative of the constant function (y) is equal to zero.