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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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$derivdef\left(2^2x^2\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (2x)^2 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 2^2. Find the derivative of 4x^2 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 4x^2. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(x+h\right)^2.