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Find the derivative of $2x^2+5x-12$ 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 $2x^2+5x-12$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{2\left(x+h\right)^2+5\left(x+h\right)-12-\left(2x^2+5x-12\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Factor the expression 2x^2+5x+-12. Find the derivative of 2x^2+5x-12 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^2+5x-12. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 5 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(2x^2+5x-12\right). Add the values -12 and 12.