Exercise
$\frac{d}{dx}e^{x+y}=e^{xy}+e^x-e^y$
Step-by-step Solution
Learn how to solve problems step by step online. Find the implicit derivative d/dx(e^(x+y)=e^(xy)+e^x-e^y). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. 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 a sum of two or more functions is the sum of the derivatives of each function.
Find the implicit derivative d/dx(e^(x+y)=e^(xy)+e^x-e^y)
Final answer to the exercise
$y^{\prime}=\frac{e^x-e^y-e^{\left(x+y\right)}+ye^{xy}}{e^{\left(x+y\right)}-xe^{xy}}$