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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 $\log \left(4x\right)$ 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 $\log \left(4x\right)$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\log \left(4\left(x+h\right)\right)-\log \left(4x\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of log(x+-3)+log(x+2)=log(4*x) using the definition. Find the derivative of \log \left(4x\right) 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 \log \left(4x\right). Substituting f(x+h) and f(x) on the limit, we get. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Expand the fraction \frac{x+h}{x} into 2 simpler fractions with common denominator x. Simplify the resulting fractions.