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The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function
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$10\frac{d}{dx}\left(\left(5x^2+1\right)^2x\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (5x^2+1)^210x. 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=. The derivative of the linear function is equal to 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}.