Final Answer
Step-by-step Solution
Specify the solving method
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=e^x\left(1+x\right)^3$
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$\frac{d}{dx}\left(x\right)e^x\left(1+x\right)^3+x\frac{d}{dx}\left(e^x\left(1+x\right)^3\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of xe^x(1+x)^3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=e^x\left(1+x\right)^3. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^x and g=\left(1+x\right)^3. The derivative of the linear function is equal to 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.