Final answer to the problem
$e^x\left(1+x\right)$
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Step-by-step Solution
How should I solve this problem?
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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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1
Since the exponent of the denominator is negative, we can bring it to the numerator and thus simplify
Learn how to solve quotient rule of differentiation problems step by step online.
$\frac{d}{dx}\left(xe^x\right)$
Learn how to solve quotient rule of differentiation problems step by step online. Find the derivative d/dx(x/(e^(-x))). Since the exponent of the denominator is negative, we can bring it to the numerator and thus simplify. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=e^x. The derivative of the linear function is equal to 1. Applying the derivative of the exponential function.
Final answer to the problem
$e^x\left(1+x\right)$
