Final answer to the problem
$x^2e^x\left(3+x\right)$
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Step-by-step Solution
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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
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^3$ and $g=e^x$
Learn how to solve implicit differentiation problems step by step online.
$\frac{d}{dx}\left(x^3\right)e^x+x^3\frac{d}{dx}\left(e^x\right)$
Learn how to solve implicit differentiation problems step by step online. Find the derivative of x^3e^x. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^3 and g=e^x. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Subtract the values 3 and -1. Applying the derivative of the exponential function.
Final answer to the problem
$x^2e^x\left(3+x\right)$
