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The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: $(a+b)(a-b)=a^2-b^2$.
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$derivdef\left(\left(2x\right)^2-9\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (2x+3)(2x-3) using the definition. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. The power of a product is equal to the product of it's factors raised to the same power. Find the derivative of 4x^2-9 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^2-9. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -1 by each term of the polynomial \left(4x^2-9\right).