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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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$4\frac{d}{dx}\left(\left(x+5\right)^2\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 3(x-2)^2+8(7+5x)=4(x+5)^2. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. 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 the constant function (5) is equal to zero.