## Step-by-step Solution

Problem to solve:

Solving method

Learn how to solve problems step by step online.

$\frac{d}{dx}\left(\left(x^3+2\right)^2\right)\left(x^4+4\right)^4+\left(x^3+2\right)^2\frac{d}{dx}\left(\left(x^4+4\right)^4\right)$

Learn how to solve problems step by step online. Find the derivative using the product rule (d/dx)((x^3+2)^2(x^4+4)^4). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x^3+2\right)^2 and g=\left(x^4+4\right)^4. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-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}. The derivative of a sum of two functions is the sum of the derivatives of each function.