## Step-by-step Solution

Problem to solve:

Solving method

Learn how to solve differential calculus problems step by step online.

$\frac{1}{\sqrt{xe^{2x}}}\frac{d}{dx}\left(\sqrt{xe^{2x}}\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of ln((xe^(2x))^0.5). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{x} and g=e^x.