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Find the derivative of $\log_{7}\left(3x\right)$ 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 $\log_{7}\left(3x\right)$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\log_{7}\left(3\left(x+h\right)\right)-\log_{7}\left(3x\right)}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of log7(3*x) using the definition. Find the derivative of \log_{7}\left(3x\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_{7}\left(3x\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.