Exercise
$\frac{d}{dx}+\frac{2}{x+2}y=\frac{2}{\left(x+2\right)^4}$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(2/(x+2)y=2/((x+2)^4)). Multiply the fraction by the term . Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. 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}}. 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}}.
Find the implicit derivative d/dx(2/(x+2)y=2/((x+2)^4))
Final answer to the exercise
$\frac{2y^{\prime}\left(x+2\right)-2y}{\left(x+2\right)^2}=\frac{-8}{\left(x+2\right)^{5}}$