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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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$derivdef\left(2^3x^3\right)$
Learn how to solve problems step by step online. Find the derivative of (2x)^3 using the definition. The power of a product is equal to the product of it's factors raised to the same power. Calculate the power 2^3. Find the derivative of 8x^3 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 8x^3. Substituting f(x+h) and f(x) on the limit, we get. The cube of a binomial (sum) is equal to the cube of the first term, plus three times the square of the first by the second, plus three times the first by the square of the second, plus the cube of the second term. In other words: (a+b)^3=a^3+3a^2b+3ab^2+b^3 = (x)^3+3(x)^2(h)+3(x)(h)^2+(h)^3 =.