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The derivative of a function multiplied by a constant ($3$) is equal to the constant times the derivative of the function
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$3\frac{d}{dx}\left(x^2\left(x^5-8\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 3x^2(x^5-8). The derivative of a function multiplied by a constant (3) 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^2 and g=x^5-8. 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.