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The power of a product is equal to the product of it's factors raised to the same power
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$derivdef\left(64x^3-x\right)$
Learn how to solve problems step by step online. Find the derivative of f(x)=(4x)^3-x using the definition. The power of a product is equal to the product of it's factors raised to the same power. Find the derivative of 64x^3-x using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is 64x^3-x. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -1 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(64x^3-x\right).