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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
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$2\left(2x^3y^8-6x^2\right)\frac{d}{dx}\left(2x^3y^8-6x^2\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (2x^3y^8-6x^2)^2. 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 function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^3 and g=y^8.