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How should I solve this problem?
- 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 $\frac{x^2}{x-1}$ 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 $\frac{x^2}{x-1}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve definition of derivative problems step by step online.
$\lim_{h\to0}\left(\frac{\frac{\left(x+h\right)^2}{x+h-1}-\frac{x^2}{x-1}}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (x^2)/(x-1) using the definition. Find the derivative of \frac{x^2}{x-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 \frac{x^2}{x-1}. Substituting f(x+h) and f(x) on the limit, we get. Combine \frac{\left(x+h\right)^2}{x+h-1}-\frac{x^2}{x-1} in a single fraction. Combine \left(x+h\right)^2+\frac{-x^2\left(x+h-1\right)}{x-1} in a single fraction. Divide fractions \frac{\frac{\frac{-x^2\left(x+h-1\right)+\left(x+h\right)^2\left(x-1\right)}{x-1}}{x+h-1}}{h} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.
