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When multiplying exponents with same base we can add the exponents
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$derivdef\left(2x\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 2x^1/2x^1/2 using the definition. When multiplying exponents with same base we can add the exponents. Find the derivative of 2x 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 2x. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 2 by each term of the polynomial \left(x+h\right). Simplifying.