## Step-by-step explanation

Problem to solve:

Learn how to solve implicit differentiation problems step by step online.

$\frac{d}{dx}\left(x\sqrt{1+y}+\sqrt{y\left(1+2x\right)}\right)=\frac{d}{dx}\left(2x\right)$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)(x(1+y)^0.5+(y(1+2x))^0.5=2x). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1.