Final Answer
Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=e^{-x}$ and $g=\ln\left(x\right)$
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$\frac{d}{dx}\left(e^{-x}\right)\ln\left(x\right)+e^{-x}\frac{d}{dx}\left(\ln\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of e^(-x)ln(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{-x} and g=\ln\left(x\right). 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}. Multiply the fraction and term. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.