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Find the derivative of $10\ln\left(x\right)$ 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 $10\ln\left(x\right)$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{10\ln\left(x+h\right)-10\ln\left(x\right)}{h}\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative of y=10ln(x) using the definition. Find the derivative of 10\ln\left(x\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 10\ln\left(x\right). Substituting f(x+h) and f(x) on the limit, we get. Factor the polynomial 10\ln\left(x+h\right)-10\ln\left(x\right) by it's greatest common factor (GCF): 10. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}. 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).