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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\left(x^4+2\right)^2$ and $g=\left(x^5+4\right)^4$
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$\frac{d}{dx}\left(\left(x^4+2\right)^2\right)\left(x^5+4\right)^4+\left(x^4+2\right)^2\frac{d}{dx}\left(\left(x^5+4\right)^4\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (x^4+2)^2(x^5+4)^4. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\left(x^4+2\right)^2 and g=\left(x^5+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 or more functions is the sum of the derivatives of each function.