Final answer to the problem
Step-by-step Solution
Specify the solving method
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
Learn how to solve product rule of differentiation problems step by step online.
$\frac{d}{dx}\left(x\right)e^x\left(1+x\right)^3+x\left(\frac{d}{dx}\left(e^x\right)\left(1+x\right)^3+e^x\frac{d}{dx}\left(\left(1+x\right)^3\right)\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(xe^x(1+x)^3). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. 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}. Applying the derivative of the exponential function.