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Find the derivative of $9x^2-2x-1$ 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 $9x^2-2x-1$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{9\left(x+h\right)^2-2\left(x+h\right)-1-\left(9x^2-2x-1\right)}{h}\right)$
Learn how to solve simplification of algebraic expressions problems step by step online. Factor the expression 9x^2-2x+-1. Find the derivative of 9x^2-2x-1 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 9x^2-2x-1. Substituting f(x+h) and f(x) on the limit, we get. Factoring by -1. Subtract the values 1 and -1. Multiply the single term -2 by each term of the polynomial \left(x+h\right).