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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 $\left(5x+\frac{1}{2}\right)^2$ 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 $\left(5x+\frac{1}{2}\right)^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(5\left(x+h\right)+\frac{1}{2}\right)^2-\left(5x+\frac{1}{2}\right)^2}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of (5x+1/2)^2 using the definition. Find the derivative of \left(5x+\frac{1}{2}\right)^2 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 \left(5x+\frac{1}{2}\right)^2. Substituting f(x+h) and f(x) on the limit, we get. Expand the expression \left(5\left(x+h\right)+\frac: (a+b)^2=a^2+2ab+b^2{2}\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Multiply the single term 5 by each term of the polynomial \left(x+h\right). Expand the expression \left(x+h\right)^{2} using the square of a binomial: (a+b)^2=a^2+2ab+b^2.