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Find the derivative of $x^2+x-6$ 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 $x^2+x-6$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(x+h\right)^2+x+h-6-\left(x^2+x-6\right)}{h}\right)$
Learn how to solve problems step by step online. Factor the expression x^2+x+-6. Find the derivative of x^2+x-6 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 x^2+x-6. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(x+h\right)^2. Solve the product -\left(x^2+x-6\right). Cancel like terms x^2 and -x^2.