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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(\left(3x-2\right)^{10}\right)\left(5x^2-x+1\right)^{12}+\left(3x-2\right)^{10}\frac{d}{dx}\left(\left(5x^2-x+1\right)^{12}\right)$
Learn how to solve differential calculus problems step by step online. Simplify the expression g(x)=(3x-2)^10(5x^2-x+1)^12. 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 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.