Exercise
$\frac{d}{dx}\left(xe^y+3x=3e^{\left(\frac{y}{3}\right)}\right)$
Step-by-step Solution
Learn how to solve integral calculus problems step by step online. Find the implicit derivative d/dx(xe^y+3x=3e^(y/3)). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Applying the derivative of the exponential function. The derivative of a function multiplied by a constant (\frac{1}{3}) is equal to the constant times the derivative of the function.
Find the implicit derivative d/dx(xe^y+3x=3e^(y/3))
Final answer to the exercise
$e^y+xe^y+3=e^{\frac{y}{3}}y^{\prime}$