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When multiplying two powers that have the same base ($x$), you can add the exponents
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$derivdef\left(4x^2\frac{4d}{dx}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 4(4d)/dxxx using the definition. When multiplying two powers that have the same base (x), you can add the exponents. Find the derivative of 4x^2\frac{4d}{dx} 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\frac{4d}{dx}. Substituting f(x+h) and f(x) on the limit, we get. Multiplying the fraction by 4\left(x+h\right)^2. Multiplying the fraction by -4x^2.