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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=
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$\frac{d}{dx}\left(4x+1\right)\left(2x^2+x-3\right)^4+\left(4x+1\right)\frac{d}{dx}\left(\left(2x^2+x-3\right)^4\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (4x+1)(2x^2+x+-3)^4. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. 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. The derivative of a sum of two or more functions is the sum of the derivatives of each function.