Exercise
$\frac{d}{dx}xe^y=x-y+y^2$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(xe^y=x-yy^2). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=e^y. The derivative of the linear function is equal to 1. Applying the derivative of the exponential function.
Find the implicit derivative d/dx(xe^y=x-yy^2)
Final answer to the exercise
$y^{\prime}=\frac{1-e^y-xe^y}{1-2y}$