Final Answer
Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^4+x-2$ and $g=\left(-8x^2+1\right)^6$
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$\frac{d}{dx}\left(x^4+x-2\right)\left(-8x^2+1\right)^6+\left(x^4+x-2\right)\frac{d}{dx}\left(\left(-8x^2+1\right)^6\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (x^4+x+-2)(-8x^2+1)^6. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^4+x-2 and g=\left(-8x^2+1\right)^6. 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.