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- Find the derivative using the definition
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Prove from LHS (left-hand side)
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Find the derivative of $\frac{1}{6}x^2-\frac{2}{3}x-\frac{3}{13}$ 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 $\frac{1}{6}x^2-\frac{2}{3}x-\frac{3}{13}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve special products problems step by step online.
$\lim_{h\to0}\left(\frac{\frac{1}{6}\left(x+h\right)^2-\frac{2}{3}\left(x+h\right)-\frac{3}{13}-\left(\frac{1}{6}x^2-\frac{2}{3}x-\frac{3}{13}\right)}{h}\right)$
Learn how to solve special products problems step by step online. Find the derivative of y=1/6x^2-2/3x+-3/13 using the definition. Find the derivative of \frac{1}{6}x^2-\frac{2}{3}x-\frac{3}{13} 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 \frac{1}{6}x^2-\frac{2}{3}x-\frac{3}{13}. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -\frac{2}{3} by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(\frac{1}{6}x^2-\frac{2}{3}x-\frac{3}{13}\right). Add the values -\frac{3}{13} and \frac{3}{13}.