Step-by-step Solution

Derive the function $\ln\left(\sqrt{xe^{2x}}\right)$ with respect to x

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Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(\ln\left(\sqrt{x e^{2x}}\right)\right)$

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

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

Unlock this full step-by-step solution!

Learn how to solve differential calculus problems step by step online. Derive the function ln((x*2.718281828459045^(2*x))^0.5) with respect to x. 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.

Final Answer

$\frac{\frac{1}{2}e^x+xe^x}{xe^x}$

Problem Analysis

$\frac{d}{dx}\left(\ln\left(\sqrt{x e^{2x}}\right)\right)$

Main topic:

Differential calculus

Related formulas:

3. See formulas

Time to solve it:

~ 0.1 seconds