Final Answer
Step-by-step Solution
Specify the solving method
Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve logarithmic differentiation problems step by step online.
$\frac{d}{dx}\left(\frac{1}{2}\ln\left(xe^{2x}\right)\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln((xe^(2x))^1/2)). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Apply the formula: \ln\left(e^x\right)=x, where x=2x. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.